J. Chem. SOC., Faraday Trans. 2, 1985, 81, 705-716

Conformational Transitions in Polymethacrylates Effect of the Side Chain

BY ISSA A. KATIME" AND MARIA TERESA GARAY

Departamento de Quimica Fisica, Grupo de Propiedades Termodiniimicas de MacromolCculas en Disoluci6n, Universidad del Pais Vasco, Apartado 644, Bilbao, Spain

AND JEANNE FRANCOIS Centre de Recherches sur les Macromolecules, C.N.R.S., 6 rue Boussingault, 67083 Strasbourg

Cedex, France

Received 21 st August, 1984

The temperature dependences of viscometric, refractometric and densitometric data have been studied for several polymethacrylates: poly(methy1 methacrylate), poly(isobuty1 methacrylate), poly(pheny1 methacrylate) and poly( cyclohexyl methacrylate) in methyl isobutyl kktone solution. It has been found that these polymers change their conformation over specific temperature ranges, as evidenced by sharp changes of the unperturbed dimensions ( K O ) , refractive-index increment (dnldc) and partial specific volume (&). The influence of the side group, particularly its nature and size, on the phenomenon has also been studied.

The results for poly(cyclohexy1 methacrylate) are particularly interesting. The nature of the side group in this polymer allows a contribution from the side chain to the main-chain conformational transition.

Finally, several semi-empirical relations have been proposed which correlate different thermodynamic parameters.

It is well known that a polymeric molecule can adopt a great number of different conformations as a consequence of its chemical constitution and its great length. Each C-C bond must form a well defined angle close to 109" with the preceding one, a great number of different positions on the valence cone being possible. All different positions, however, are not equally probable because of various attractive and repulsive forces arising from other elements of the chain. Thus, the rotational potential energy of a bond in a polymer is characterized by three minima of different depths, the trans and the two gauche positions, which means that the chain units can adopt only some preferred positions in the valence cone giving rotational isomers.

Different models have been proposed to represent polymer conformations, for example the rotational isomeric model,' which considers the macromolecule to be a mixture of rotational isomers in equilibrium and infernal rotation to be rotational isomerization, i. e. the macromolecule is a unidimensional cooperative model.

Some macromolecules adopt different conformations under different thermody- namic or chemical conditions. The conformation of a macromolecule which is stable under determined external conditions may become unstable when these conditions change, i.e. some macromolecules undergo conformational transitions which are dependent upon external conditions. However, these conformational changes occur very rapidly and it is difficult to establish their mechanism. They become evident as a large change occurs in the equilibrium molecular properties resulting from small changes in the environmental conditions, leading to the concept of conforma- tional transition as a cooperative phenomenon.*

705

Publ

ishe

d on

01

Janu

ary

1985

. Dow

nloa

ded

by N

orth

Dak

ota

Stat

e U

nive

rsity

on

29/1

0/20

14 2

3:21

:16.

View Article Online / Journal Homepage / Table of Contents for this issue

706 CONFORMATIONAL TRANSITIONS IN POLYMETHACRYLATES

The number of synthetic polymers known to suffer conformational changes has been steadily increasing. In all cases this phenomenon appears upon the change of an intensive parameter, i.e. temperat~re,~- ' solvent composition in binary mix- tures,12-16 pH17 etc. These have a common characteristic: a sudden increase of the flexibility of the polymer.6-' '

The nature of these conformational transitions and the reasons for their existence are not sufficiently clarified. Ever since Reiss and Benoit3 detected the existence of a conformational transition in polystyrene, this subject has been studied in several l abo ra to r i e~~- '~ in order to establish the factors (effect of ~ o l v e n t , ~ - ~ polymer tac- ticity,18 nature of the solvent mixture,12-16 etc.) which cause it.

The influence of the polymer side chain remains to be studied. This contribution is very important for the family of polymethacrylates, since they contain a carboxy group which can establish specific interactions with some solvents. These interac- tions will depend largely on the size and nature of the functional group in the side chain.

We have selected poly(methy1 methacrylate) (PMMA) and the derivatives poly(isobuty1 methacrylate) (PIBM), poly(pheny1 methacrylate) (PPHM) and poly- (cyclohexyl methacrylate) (PCHM), i.&. polymethacrylates with aliphatic, aromatic and alicyclic substituents, respectively, for our study. The solvent selected was methyl isobutyl ketone (MIBK), this one solvent being used in order that differential solvent effects are avoided and the results are comparable.

EXPERIMENTAL

Monomers were purified and dried according to classical methods. The initial PMMA, PIBM and PCHM samples were prepared by radical polymerization in benzene using 1,2-azobisisobutyronitrile as initiator. The PPHM eample was a commercial one from Aldrich.

All of the polymers were subjected to fractional precipitation. The selected solvent + non-solvent systems were benzene + methanol for PMMA and PCHM, while for PIBM the non-solvent used was a mixture of methanol+water (97% v/v). PPHM was fractionated from acetone, using isopropyl alcohol as non-solvent. The fractions obtained were purified and freeze-dried from benzene.

Selected fractions of these polymers were characterized by light scattering, viscometry and membrane osmometry, as described p r e v i o ~ s l y . ' ~ ~ ' ~ Polidispersities of the fractions were always < 1.25.

The weight-average molecular weights of the fractions of the different polymethacrylates used in this paper were in the ranges (0.46-4.7) x lo5 for PMMA, (0.53-3.57) x lo5 for PIBM, (0.44-2.18) x lo5 for PPHM and (0.85-3.95) X lo5 for PCHM.

The solvent used, methyl isobutyl ketone (MIBK), was from Merck. Viscosity measurements were carried out using a suspended-level dilution viscometer as

described p r e v i ~ u s l y . ' ~ The kinetic-energy correction was (0.1 YO and therefore was neglected. The viscometer was reproducibly positioned by means of a three-point suspended system. The temperature of the water bath was regulated to i~0.05 "C.

Determinations of intrinsic viscosities were made by extrapolating plots of in (q,/ c ) and q s , / c against concentration to infinite dilution, as both plots gave the same intercept. Intrinsic-viscosity values are expressed in cm3 g- ' .

Refractive-index increments, dnldc, were measured using a Brice-Phoenix differential refractometer at 546 nm and employing a sealed-type differential cell with ground-glass stoppers to prevent loss of solvent. Temperature control was by introduction of a thermometer inside the housing, close to the cell. The calibration was performed using aqueous solutions of highly purified KCI. The calibration was checked by determining dn/dc for polystyrene in methyl ethyl ketone, cyclohexane and toluene at various temperatures.

Partial specific volumes of the polymer, ij2, were obtained from density measurements using an automatic densimeter, DMA 02 of the Kratky type, previously calibrated against

Publ

ishe

d on

01

Janu

ary

1985

. Dow

nloa

ded

by N

orth

Dak

ota

Stat

e U

nive

rsity

on

29/1

0/20

14 2

3:21

:16.

View Article Online

I. A. KATIME, M. T. G A M Y A N D J. FRANCOIS

I I I 1 I 1

0'701 0.66 r / ;wo.5.4 [I E

/ PMMA

< n c- U

0.5

707

5 15 25 35 45 55 65 T/"C

Fig. 1. Thermal variation of [ T ] for PMMA, PIBM, PPHM and PCHM in MIBK.

air and water. The temperature was controlled using a Hewlett-Packard quartz thermometer connected at the cell outlet. After improvement of the we were able to obtain an accuracy in ij2 of cm3 g-'.

RESULTS AND DISCUSSION

VISCOMETRIC MEASUREMENTS

The thermal variation of intrinsic viscosity presents anomalous behaviour, although not similar, for all the systems studied. Fig. 1 shows an example of this variation for a fraction of each of the polymers studied. For polymers PMMA, PIBM and PPHM, these variations are more noticeable the higher the molecular weight. For PCHM, the observed variations are more marked for low molecular weights. It is not possible to find the exact location of the temperature interval where the conformational transition occurs from these curves.

The anomalies observed could be caused by changes in the interactions in the system. In a macromolecular solution, the interactions are ( a ) short range, represen- ted by the unperturbed dimension, KO, and ( b ) long range, included in the second virial coefficient, A,, or some related parameter, B.

The conformational transition could originate because of changes in the short- range or/and long-range interactions. Determination of the nature and magnitude of this phenomenon is possible by application of one of the excluded-volume theories, which allow the determination of K , and B, separately, from the values

Publ

ishe

d on

01

Janu

ary

1985

. Dow

nloa

ded

by N

orth

Dak

ota

Stat

e U

nive

rsity

on

29/1

0/20

14 2

3:21

:16.

View Article Online

708 CONFORMATIONAL TRANSITIONS IN POLYMETHACRYLATES

5-

I I I

B M

of [q] obtained for the different molecular-weight fractions. In this work we have used the graphical method based on the Stockmayer-Fixman theory, according to the relation21

[ ~ 1 M - l ’ ~ = K , 4- 0.5 1 moBM (1) where m0 is the Flory-Fox constant, [7] is the intrinsic viscosity, M is the molecular weight and K , is defined as @ 0 ( ( r i ) / M ) 3 / 2 , where ( I ; ) is the root-mean-square unperturbed end-to-end distance.

In theory, K , remains constant with temperature or varies only slightly. The thermal variation of K , for these systems is shown in fig. 2 and 3. A sudden decrease in this parameter is observed, which means an increase in the flexibility of the chain. This can be explained by the occurrence of a conformational change. The tem- perature interval where this phenomenon occurs is well defined, and it is also possible to determine its magnitude: 9% for PMMA, 8% for PIBM, 26% for PPHM and 47% for PCHM (these values were calculated with respect to the KO value before the transition).

If we consider PMMA, conformational transitions of different magnitudes have been found in a great number of solvents. Thus, table 1 shows the conformational transitions of PMMA in single solvents, their magnitude being expressed as A& (O/O); values of KO before the transition and dielectric constants of the various solvents at 298 K are also given. The magnitude of the transition in MIBK is lower than that observed in the majority of solvents used.

Dondos and Benoit” have suggested that the unperturbed dimensions of polymer molecules, K,, depend on the dielectric constant, E, of the solvent in which the molecule is embedded. Particularly, they found that the larger the dielectric constant, the lower the value of Ke. The results of table 1 confirm their conclusions. Moreover,

Publ

ishe

d on

01

Janu

ary

1985

. Dow

nloa

ded

by N

orth

Dak

ota

Stat

e U

nive

rsity

on

29/1

0/20

14 2

3:21

:16.

View Article Online

I. A. KATIME, M. T. GARAY AND J. FRANCOIS 709

4 PCHM

-

PPHM

5 15 25 35 45 T/"C

Fig. 3. Variation of K , with temperature for PPHM and PCHM in MIBK.

Table 1. Conformational transitions of PMMA in different solvents

solvent K,/ 1 o4

cm3 m 0 1 ~ / 2 g-3/2 AK, (Yo) & ref.

dioxane benzene toluene butyl acetate ethyl acetate ethyl benzoate MIBK methyl benzoate

7.85 6.60 6.59 5.75 5.65 5.93 5.80 5.88

24 21 21 15.6 11.5 10.6 9 8.2

2.209 2.274 2.379 4.27 6.02 4.73

12.80 6.08

22 23 23 9 9

24 9

24

the magnitude of the transition seems to be related to the dielectric constant of the solvent in the sense that the larger the dielectric constant the smaller the trahsition.

For PIBM in MIBK the magnitude of the transition is slightly lower. The side chain, in this case, includes an isobutyl group, which is both more bulky and branched. A conformational transition in the main chain involves its reorganization. This includes the side chains which, in this case, restrict the magnitude of the transition.

The observed change for PPHM is larger. The nature of the side chain makes it possible that specific interactions between neighbouring phenyl rings create structures of groups of chain units. The observed transition may occur because, on

Publ

ishe

d on

01

Janu

ary

1985

. Dow

nloa

ded

by N

orth

Dak

ota

Stat

e U

nive

rsity

on

29/1

0/20

14 2

3:21

:16.

View Article Online

710 CONFORMATIONAL TRANSITIONS I N POLYMETHACRYLATES

Table 2. Influence of the side chain on the thermal localization of conformational transitions for several polymethacrylates

polymer A T/"C Mo ref.

poly(methy1 methacrylate) poly( ethyl methacrylate) poly( isobutyl methacrylate) poly( phenyl methacrylate) poly( cyclohexyl methacrylate) poly(cyclohexylmethy1 methacrylate) poly(4-t-butylphenyl methacrylate) poly( 4-t-butylcyclohexyl methacrylate) poly[4-( 1 , I ,3,3-tetramethylbutyl)phenyl

methacry late]

45-55 40-45 25-30 25-35 10-30 5-15

10-20 5-15

10-20

100 114 142 162 168 182 218 224

274

9, 23, 24 5, 31

this work 19 10 30 1 1 30

1 1

increasing the temperature, the cooperative stabilization of the chain units is no longer possible, thus producing a sudden change in the mobility of the side chains.26-28 The existence of helical sequences is also possible in this polymer and could lead to a greater change in the parameter KO, since the conformational change is not only of the type disorder- disorder but also involves an order- disorder transition.

The behaviour of PCHM in MIBK is different. Conformational transitions in a synthetic polymer become evident on a sudden decrease in the unperturbed dimensions resulting from increased chain flexibility. In this polymer, once the transition has occurred, a continued increase in temperature produces a progressive decrease in flexibility until a stable value is reached which is lower than the initial one. The magnitude of the change in KO, initially 47%, is reduced until a final value of 16% is reached. Thus it appears that, besides the conformational change, another change is taking place.

The side chain of this polymer includes a cyclohexyl group. It is well known that monosubstituted cyclohexane can adopt two different chair conformations. The one substituted in an equatorial orientation has a lower energy. The other, substituted in the axial position, presents a greater packing problem, which therefore increases its energy content.29 The energy difference between them is low and at room temperature there is a rapid interchange, tending to an equilibrium between both conformers which is shifted with increasing temperature towards the axial conformer. It appears that similar behaviour can occur in PCHM, thus provoking an increase in the steric interactions of the polymer. This could explain the increase in rigidity observed starting from 288 K.

Similar behaviour has been found for a derivative, poly( cyclohexylmethyl metha~rylate).~' Thus it appears that in polymethacrylates whose side chains contain a cyclohexyl group, conformational transitions are considerably influenced by addi- tional conformational changes of the side chains.

The temperature interval, AT where the transition occurs for the polymers of this work and for some others from the literature are listed in table 2, where Mo is the molecular weight of the side chain. These results indicate that the temperature interval where the transition occurs is shifted towards lower temperatures as the size of the polymer side chain increases.

As to the variation of the B parameter with temperature, different behaviour is observed. Thus, the polymethacrylates with aliphatic substituents, PMMA and

Publ

ishe

d on

01

Janu

ary

1985

. Dow

nloa

ded

by N

orth

Dak

ota

Stat

e U

nive

rsity

on

29/1

0/20

14 2

3:21

:16.

View Article Online

3 -

N I M

N - 3

% N

2 2- --. lg

I. A. KATIME, M. T. G A M Y AND J. FRANCOIS 71 1

8

N

I on 7 %

E

2

3 m

G- 6

15 2 5 35 45

Fig. 4. Plot of interaction parameter B against temperature for PMMA and PIBM in MIBK. T / "C

7

6 N

I on

3

2

5 15 25 35 45 T / "C

Fig. 5. Plot of interaction parameter B against temperature for PPHM and PCHM in MIBK.

Publ

ishe

d on

01

Janu

ary

1985

. Dow

nloa

ded

by N

orth

Dak

ota

Stat

e U

nive

rsity

on

29/1

0/20

14 2

3:21

:16.

View Article Online

712

0.18

- 0.16 I

," - E 2 0.12

z -u (E --.

0.1 0

0.08

CONFORMATIONAL TRANSITIONS I N POLYMETHACRYLATES

I

5 15 25 35 4 5 55 T I T

Fig. 6. Variation with temperature of refractive-index increment, dnldc, of PMMA, PIBM, PPHM and PCHM in MIBK.

PIBM (fig. 4), in MIBK show similar increases of B with temperature; the same effect occurs for other

The other polymers, PPHM and PCHM (fig. 9, behave differently from each other and from the polymethacrylates with alkyl side chains. Thus, for PPHM great irregularities are observed, which can be explained if we take into account that the transition begins close to the 6 temperature, where variations in behaviour The rupture of interactions between phenyl rings favours the entrance of solvent into the macromolecular coil, so that the carbonyl group of the solvent can interact with the active groups of the macromolecule leading to an increase in the B parameter.

The results for PCHM are very different, as was expected. Because of steric hindrance, interaction of the carboxy group with the solvent is decreased when this group is in the axial position of the cycloheyme ring. It follows that the interaction with solvent decreases when there ; , a shift from the equatorial to the axial conforma- tion. This explains the decrease in B with increasing temperature, starting at ca.

Finally, these results indicate that the side chain plays an important role in the temperature of the transition, as well as in the magnitude, depending on the nature and size of the side chain.

288 K.

REFRACTOMETRIC A N D DENSIMETRIC MEASUREMENTS

Refractometric measurements confirm the validity of this technique for the detection of conformational transitions. The variations of the refractive-index incre- ment, dnldc, with temperature for all the systems studied are shown in fig. 6 . As

Publ

ishe

d on

01

Janu

ary

1985

. Dow

nloa

ded

by N

orth

Dak

ota

Stat

e U

nive

rsity

on

29/1

0/20

14 2

3:21

:16.

View Article Online

I. A. KATIME, M. T. G A M Y AND J. FRANCOIS

0 ' g 6 . 0.94 Jc_________PlsM 0.89L PCHM

PMMA 0.81 -

PPHM 0.79 -

0.77 - I 1 I 1 I

15 25 35 45 55 T/"C

713

Fig. 7. Thermal variation of partial specific volume, C2, of PMMA, PIBM, PPHM and PCHM in MTBK.

can be seen, the temperature ranges where the transitions occur are similar to those obtained by viscometric measurements. Only for PMMA is the temperature interval shifted towards higher temperatures, probably because of differences in the steric content of the samples used. Thus, PMMA samples used in viscometric measure- ments have a higher syndiotactic content,'* as shown by n.m.r. measurements.

Density measurements confirm the existence and location of the transitions. Fig. 7 shows the thermal variation of the partial specific volume of the polymer, i j 2 , for all the systems studied.

The shape of the plot for PCHM at temperatures >313 K is interesting. It is paralleled by the dn/dc plot for PCHM and could be caused by a new conformation change.

The independent measurements of refractive-index increment and partial specific volume allow the partial specific refractivity of all the polymers to be evaluated. The Lorenz-Lorentz theory, whose validity has been repeatedly ~ e r i f i e d , ~ ~ - ~ ~ has been used. The following equation was proposed:

n i - I 6no dn n0+2 (ni+2)2 dc

R2 =r ~2 +- -

where no is the refractive index of solvent, v2 is the specific volume of polymer and R2 is the specific refractivity related to polymer polarizability, given by:

From eqn (2) and (3) it is possible to obtain the partial specific refractivity, R2,t as well as the refractive index of the polymer in solution, n,*. The results for the systems studied lead to a value for the partial specific refractivity for each polymer

?When using the partial specific volume, we obtain the partial specific refractivity, Rz , and the refractive index of the polymer in solution, nf.

Publ

ishe

d on

01

Janu

ary

1985

. Dow

nloa

ded

by N

orth

Dak

ota

Stat

e U

nive

rsity

on

29/1

0/20

14 2

3:21

:16.

View Article Online

7 14 CONFORMATIONAL TRANSITIONS IN POLYMETHACRYLATES

Table 3. Partial specific refractivity and refractive index of several polymethacrylates in MIBK

polymer E2/cm3 g-' n t

PMMA PIBM PPHM PCHM

0.245 1.520 0.274 1.492 0.279 1.629 0.272 1.535

0.0

0.2

h

%" 014 \

Y v

80 - 0.6

0.8

k %.

't

0 .o 0.1 0.2 u -0.5

Fig. 8. Correlation between Mark-Houwink-Sakurada parameters for PMMA (0), PIBM (O), PPHM (m) and PCHM (0) in MIBK.

(table 3). No significative deviations of these values were observed on varying the temperature, and the results seem to indicate that there is no change in the polarizabil- ity of the polymers when conformational transitions occur. Table 3 also shows the values of the refractive index of each polymer in MIBK at 298 K and A = 546 nm.

As PMMA has been studied extensively and the existing experimental results have been checked, we compared these results with those obtained in this work. Thus, the partial specific refractivity obtained in this work, R2 = 0.245 cm3 g-', is coincident with that obtained by Bodmann3' under the same conditions. Likewise, the result n; = 1.520 obtained for PMMA is in very good agreement with that obtained by extrapolation of dn/dc values of the polymer in different solvents or solvent mixtures, n2 = 1.5 1 8,38 and slightly higher than that obtained for pure PMMA under the same conditions, n2 = 1.494.

Publ

ishe

d on

01

Janu

ary

1985

. Dow

nloa

ded

by N

orth

Dak

ota

Stat

e U

nive

rsity

on

29/1

0/20

14 2

3:21

:16.

View Article Online

I. A. KATIME, M. T. GARAY A N D J. FRANCOIS 715

0 1 2 3 4 5 B M ’ I ~ N

K*u, Fig. 9. Plot according to eqn (4).

CORRELATIONS BETWEEN SOME THERMODYNAMIC PARAMETERS

Finally, several semi-empirical relations have been proposed relating some of the parameters obtained from viscometric data. Thus, several a ~ t h o r s ~ ~ - ~ ’ have suggested that the Mark-Houwink-Sakurada parameters are not independent and they have proposed linear relations between log k and a or a function of a. The validity of these relations, however, is limited to those systems where the unperturbed dimensions parameter, KO, remains constant. In the systems of this work large variations are observed for this parameter because of the conformational change. It is possible, however, to eliminate this conformation effect by plotting log ( k / K , ) against ( a -0.5). As can be seen in fig. 8, the experimental data for our systems can be adjusted to a unique straight line.

Similarly, a linear dependence has been found for the Huggins constant, k’, starting from an equation already proposed by Abdel-him and Consider- ing K O to be a variable it follows that

where k’ is the Huggins constant obtained from plots of qsp/c against c, kb is the same constant under ideal conditions, a,, is the viscometric expansion coefficient, N is Avogadro’s number and C is a constant.

Fig. 9 shows a plot of k’a: against (BM”’N/ K oa,) for all the systems studied at each temperature. As can be seen, all the experimental points can be adjusted to a straight line and the intercept, k’,=0.4, is coincident with that given by Abdel-Azim and H ~ g l i n . ~ ’

All the evidence leads us to the conclusion that conformational transitions are general phenomena in polymers and that the hydrodynamic behaviour of macromolecular systems follows the limiting laws of polymer solutions even when the polymer undergoes a conformational change, providing that the actual conforma- tion of the polymer is taken into account.

’ T. M. Birshtein and 0. B. Ptitsyn, Conformations of Macromolecules (Interscience, New York,

’ A. J. Hopfinger, Conformational Properties of Macromolecules (Academic Press, New York, 1973). 1966).

C. Reiss and H. Benoit, C. R. Acad. Sci., 1961, 253, 268.

Publ

ishe

d on

01

Janu

ary

1985

. Dow

nloa

ded

by N

orth

Dak

ota

Stat

e U

nive

rsity

on

29/1

0/20

14 2

3:21

:16.

View Article Online

716 CONFORMATIONAL TRANSITIONS IN POLYMETHACRYLATES

V. E. Eskin and I. N. Serdjuk, J. Polym. Sci., Part C, 1968; 23, 309. ' P. Vasudevan and M. Santappa, Mukromol. Chem., 1970, 137, 261. ' A. Dondos, Mukromol. Chem., 1970, 135, 181.

P. Karayannidis and A. Dondos, Mukromol. Chem., 1970, 147, 135. A. Dondos, P. Rempp and H. Benoit, Mukromol. Chem., 1973, 171, 135. 1. Katime, C. Ramiro and J. E. Figueruelo, Eur. Polym. J., 1977, 13, 451; I. Katime and M. T. Garay, Br. Polym. J., 1983, 15, 117.

lo I. Katime, X. Ibarra, M. T. Garay and R. Valenciano, Eur. Polym. J., 1981, 17, 509. I ' C. Sarabia, D. Radic and L. Gargallo, Mukromol. Chem., 1981, 182, 2517. I 2 I. Katime, R. Valenciano and T. Nuho, Polym. Bull., 1982, 6, 437. l 3 A. Dondos, H. Havredaki and A. Mitsou, Mukromol. Chern., 1975, 176, 1481. I 4 L. Gargallo, Mukromol. Chem., 1976, 177, 233. I' A. Mitsou-Clappas and K. Viras, Eur. Polym. J., 1980, 16, 205. l 6 1. Katime, L. C. Cesteros and J. R. Ochoa, Polym. Bull., 1982, 6, 447.

M. Mandel and 3. C. Leyte, J. Polym. Sci., 1962, 56, 523; J. Polym. Sci., Part A , 1964, 2, 1879. I. Katime, P. Gutierrez Cabaiias, J. R. Ochoa, M. T. Garay and C. Ramiro, Polymer, 1983,24, 1015.

17

18

l9 I. Katime and M. T. Garay, to be published. 2o D. Sarazin. J. Le Moigne and J. Francois, J. Appl. Polym. Sci., 1978, 22, 1377. 2 1 W. H. Stockmayer and M. Fixman, J. Polym. Sci., Parr C, 1963, 1, 137. 22 A. Dondos and H. Benoit, C. R. Acud. Sci., Ser. C, 1970, 271, 1055. 23 I. Katime, A. Roig and P. Gutierrez Cabanas, Eur. Polym. J., 1974, 10, 897. 24 I. Katime and C. Ramiro Vera, Eur. Polym. J., 1977, 13, 783. 25 A. Dondos and H. Benoit, Macromolecules, 1971, 4, 279.

27 C. Noel, N. Platzer, L. Monnerie and J. Basselier, J. Chim. Phys., 1970, 67, 558. 28 J. B. Helms and G. Challg, J. Polym. Sci., Purr A, 1972, 10, 1447. 29 M. Hannak, Conformation Theory (Academic Press, New York, 1965). 30 L. Gargallo, I. Mendez and D. Radic, Mukromol. Chem., 1983, 184, 1053. 3 1 J. Y. Olayemi, Mukromol, Chem., 1982, 183, 2547. 32 D. Sarazin and J. Francois, Polymer, 1978, 19, 699. 33 P. G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, N.Y., 1979). 34 F. Candau, C. Dufour and J. Francois, Mukromol. Chem., 1976, 177, 3359. 35 W. Heller, J. Phys. Chem., 1965, 69, 1123. 36 M. B. H u g h , J. Appl. Polym. Sci., 1965, 9, 4003. 37 V. 0. Bodmann, Mukromol. Chem., 1969, 122, 196; 210. 38 M. T. Garay, Ph.D. Thesis (Universidad del Pais Vasco, 1984). 3u K. Kamide, A. Kataoka and T. Kawai, Mukromol. Chem., 1971, 139, 221. 40 P. Munk and M. E. Halbrook, Macromolecules, 1976, 9, 441. 4 1 F. Millich, E. W. Hellm.uth and S. Y. Huang, J. Polym. Sci., Polym. Chem. Ed., 1975, 13, 2143. 42 A. A. Abdel -h im and M. B. H u g h , Mukromol. Chem., Rapid Commun., 1981, 2, 119.

K. J. Liu and R. Ullman, Polymer, 1965, 6, 100. 26

(PAPER 4/ 146 1 )

Publ

ishe

d on

01

Janu

ary

1985

. Dow

nloa

ded

by N

orth

Dak

ota

Stat

e U

nive

rsity

on

29/1

0/20

14 2

3:21

:16.

View Article Online