Effect of branching on the physical characteristics of polymers

Effect o f branching on p o l y m e r s

1821

REFERENCES 1. V. V. KORSHAK and T. M. FRUNZE, Sintetichesdkie geterotsennye poliamidy (Synthetic Heterochain Polyamides). Moscow, 1962. 2. D. E. FLOID, Polyamidy (Polyamines). Moscow, 1960. 3. V. A. DUBAK and E. T. LAZARENKO, Polyamidy i ikh primenenie pri izgotovlenii pechatnykh form (Polyamides and their Use in the Manufacture of Printing Moulds). Moscow, 1973. 4. V. K. GRISHCHENKO, A. F. MASLYUK and S. S. GUDZERA, Zhidkie fotopolimerizuyushchiecya kompozitsii (Liquid Photopolymerized Compositions). Kiev, 1985. 5. C. A. DELZENE and U. LARIDON, J. Polymer Sci. 27: 1149, 1969. 6. Japanese patent application No. 51-16235, R. Zh. Khim., 14C328P. 7. S. P. PANDA, J. Sci. and Ind. Res. 35: 560, 1976. 8. Japanese patent application No. 60-124624, R. Zh. Khim. 12C585P, 1986. 9. KWAND-DUK AHN, KYOLIN IHN and ICH CHAN KWON, J. Macromolec. Sci. Chem. 23: 356, 1986. 10. A. F. AL-SAYYAB, A. T. ATTO and F. Y. SARAH, J. Chem. Soc. C, No. 19, 3360, 1971. 11. W. J. PEPPEL, J. Polymer Sci. 51: 64, 1961. 12. Spravochnik khimiya (Chemistry Handbook) 2: Moscow-Leningrad, 1964. 13. U. SERENSON and T. KEMNBEL, Preparativnye metody khimii polimerov (Preparative Methods in the Chemistry of Polymers). Moscow, 1963. 14. E. F. PRATI" and M. J. KAMLET, J. Organ. Chem. No. 28, 1366, 1963. 15. C. D. HURD and C. M. BUESS, J. Am. Chem. Soc. 78: 5667, 1956. 16. S. P. RUDNEVA, A. F. MASLYUK, N. N. KALIBABCHUK, I. M. SOPINA, L. A. SHKURENKO and I. M. SHEPELSKAYA, Sposohy informatsii na besserebryanykh nositelyakh (Methods of Recording Information on Silver-free Carriers). P. 77, Kiev, 1977. 17. A. A. BERLIN, T. Ya. KEFELI and G. V. KOROLEV, Poliefirrakrilaty (Polyester acrylates). Moscow, 1967.

PolymerScienceVol. 33, No. 9, pp. 1821-1831,1991

0965-545X/91$15.00+.00 {~)1992PergamonPressI~d

Printed in Great Britain.

EFFECT OF BRANCHING ON THE PHYSICAL CHARACTERISTICS OF POLYMERS* A . A . ASKADSKII a n d O . V. K O V R I G A A. N. Nesmeyanov Institute of Hetero-Organic Chemistry, U.S.S.R. Academy of Sciences (Received 19 October 1990)

The effects of the length and character of the branching distribution on a number of physical characteristics of polymers, i.e. the glass transition temperature, the coefficient of bulk thermal expansion, the refractive index, the Hildebrand solubility parameter, and the surface energy are analysed. It is calculated that short chain branches have the greatest effect on the physical characteristics, since they lead to a significant change in the chemical structure of the polymer system. The effect of long chain branching depends on the differences in their chemical structure from that of the main chain and to a lesser extent on the degree of long chain branching. The physical characteristics of the polymer show the sharpest changes when tree-like branching occurs. IN EARLIER p a p e r s the effect o f p o l y m e r e n d g r o u p s [1] and the d e g r e e o f cross-linking [2] on different physical characteristics o f p o l y m e r s was analysed. It was s h o w n that at small M M the effect * Vysokomol. soyed. A33: No. 9, 1945---1955,1991.

1822

A . A . ASKADSKIIand O. V. KOVRIGA

T77(c)

FIG. 1. Schematicdiagram of different typesof branching. Explanation in text. of the end groups becomes decisive, when the number of repeating units is reduced to a minimum and down to the dimer. When a network is formed the properties also change qualitatively, when the distance between cross-link nodes becomes small (a between-unit fragment contains 1-4 repeating units). In this work the effect of the branching of polymer chains on their physical properties, which is important in establishing structural materials from polymers of different MM and degree of branching, is analysed. In the general case the number of possible chain branching variants can be very large. We will consider the main variants, which are shown schematically in Fig. 1, which shows the main chain and the possible branching variants. In the simplest (but less probable) case the branches can have the same length and can be located in each repeating unit (Fig. la). Another variant corresponds to branches of the same length, uniformly distributed along the main chain at a specific number of units (Fig. 2b). A third variant corresponds to the case where there are branches of different lengths, but these are uniformly distributed along the main chain at a specific number of units (Fig. lc). Another variant is possible in which there are branches of different lengths randomly distributed along the main chain (Fig. ld). We will consider two further variants. With one of these branches of different length are randomly distributed along the main chain, and at each branch there is one further branch, but of different length (Fig. le). The appearance of each new branch here entails the appearance of one further branch. In all the cases considered the branches can have one and the same chemical nature in relation to the main chain, or a different nature. The case when the branches have a different chemical nature compared with the main polymer chain corresponds to grafted copolymers. In such systems microphase stratification generally occurs because of the thermodynamic incompatibility of the main and grafted chains. Moreover, each phase can have, for example, its own glass transition temperature, which, however, often differs from that of the individual components. The values of Tg for grafted copolymers can thus only be calculated when the original and grafted polymers are completely compatible. However, the reverse problem, i.e. evaluation of the composition of a

Effect of branching on polymers

1823

phase from the temperatures of the relaxational transitions in each phase, assuming that a specific number of extraneous units is included in each phase can be solved. These problems are outside the framework of this paper, and the properties of grafted copolymers are not considered. In homopolymers the branches can be joined directly to the main chain by substitution of one of the atoms or can be joined through a disjunction of another chemical nature. We will consider these variants with specific examples. We will select PE and its derivatives as one of the model polymers for such a consideration,

--CH2--CH--(CH2--CH~)~I (CH2) n I CHs I

We will begin the consideration with the glass transition temperature. It is noted as a preliminary, that when m = 0, we have the situation shown in Fig. la, when the branches are of the same length and are located in each repeating unit. We will consider the course of the calculation for this structure in detail. The glass transition temperature is calculated from the equation [3] Ei~V, Tg = ~,iaiAViq_ ~,ibi,

(1)

where EiAVi is the van der Waals volume of the polymer repeating unit, made up of the van der Waals volumes AVi of the individual atoms; a denotes the increments indicating the contribution of each atom to weak dispersion interaction; b~ denotes the increments indicating the contribution of individual polar groups to strong intermolecular interaction (dipole-dipole interaction and hydrogen bonds). For the structure represented above

~iAVi = 51.3 + 17.1n + 34.2m (/~3) ~iaiAVi + ~ibi = (185.34 + 80.25n + 160m) x 10 -3 (~3 K - l). In calculating the value of Y-;bi it is essential to allow for the fact that each branch leads to the necessity of introducing an increment b i. As a result we obtain 51.3 + 17.1n + 34.2m Tg, K = 185.34 + 80.25n + 160.5m x 103.

(2)

The results of the calculation made with (2) are shown in Fig. 2. It can be seen that if the branches are in each repeating unit (m = 0) then Tg is very markedly dependent on the number of CH2 groups in the branch. With decrease in n, Tg begins to increase rapidly, when n < 5. In this case the situation is similar to that observed in analysis of the effect of cross-linking frequency on the properties of frequently cross-linked polymers [2]. When m = 0 we have a series of branched polymers, the properties of which have been studied experimentally [4]. Thus, for example, when m = 0 and n -- 0, we have polypropylene, for which the calculated value of T s is 277 K, as against an experimental value of 263 K. When m = 0 and n = 1 we have polybutene-1, for which the calculated value of Ts is 258K, as against an experimental value of 248 K. Such convergence, which is characteristic of the increments method, is also observed with other polymers when m = 0 and n = 2 and 6.

1824

A . A . ASKADSKIIand O. V. KOVRIGA 7"aoC

ok -lOt-

I

\

0

"-4

i

I

I

I

I

I

I

I

I

I

5 IOn FIG. 2. Plots of the glass transition temperature Ts against n for structure I. Here and in Fig. 4 the numbers on the plots are the valuesof m.

If the branches are thinned out (m > 0), then the effect of the number of units in a branch on Tg is decreased, and when the branches become sufficiently rare (m = 10) the branch length hardly affects Tg (it is noted, however, that when m--, 0o this corresponds to a star-like polymer). The case when the branches in PE are distributed randomly along the chain, and are of different length will now be considered. We allow that the value of m obeys the random distribution law F ( m ) = 1 - e ''/m'~

(m/> 0),

(3)

where mine is the mean value of m . The distribution density function has the form 1

f(m) =

mine

(4)

e -'''~.

We allow also that the degree of polymerization of the branches obeys the Flory distribution q(.) =

(5)

where 7 = 1/nw, nw is the mean weighted value of n. For further calculations it is assumed that the limiting value of n = 10. The number of units in the branches is then given by the equation i=n K

nbr = ~, i 2 ~ e -vi.

(6)

i= 1

The equation for calculating the glass transition temperature Tg with allowance for the whole of the above for the chemical structure I has the form /=rig

j~mK

51.3+ 17.1 ~ i 2 ~ 2 e - ~ i + 34.2 ~, j ~ e -jO i~l

T, =

j=l

,-..

185.3+80.25 ~ i2y2e-Vt+160.5 ~ jfle - j # i=l j=l w h e r e / / = 1/mmc [here and in (8)-(12) the values of Tg x 10 -3 are given].

,

(7)

Effect of branching on polymers

1825

To, °C

- '/5

-5,,•

~

~

[

~

1

I

5

1

[

!0 nu,

Fro. 3. Plots of T s against n~ for structure 1. Here and in Fig. 6 the n u m b e r s on the plots are values of m.

The calculation results obtained with (7) are shown in Fig. 3. The character of the relation between Tg and nw is similar to the relation between Tg and n, with the difference only that the relation between Ts and nw is smoother than that between Tg and n. On the whole, the results of these calculations for branched PE show that the short chain branches, which are often located along the main chain, have the greatest effect on the glass transition temperature. We will pass to the next branching variant, when new branches appear in the branch itself. In this case the structural formula of branched PE has the form --CI!~--CII --(CIi~(CH2)~I (C112)x I HC--(CH~)u--CHs [ (CH~). I Clls II

This corresponds to the scheme in Fig. le. For this case the equation for Tg has the form 85.3 + 17.1(x + y + z) + 34.2m Ts = 400.97 + 80.25(x + y + z) + 160.39m - 110.8"

(8)

The significance of the symbols x, y, z, and m can be seen from the structural formula of branched PE. It is noted that if x + y + z = 0 and m = 0, then this corresponds to a polymer of the following chemical structure: --CHs--CH-I CH--CH3 I CH8

For this polymer the calculated glass transition temperature is 294 K, as against an experimental value of 302 K. Analysis of (8) shows that Ts depends only on the sum (x + y + z) and on the value of m. Figure 4a

1826

A . A . ASKADSKll and O. V. KOVRIGA

r~,*c 150

rg , °c

20~

(a)

(b)

b\ 0

50

0

7

-?0

1w 7 -"qO~

~

" (x*y÷z)

FIG. 4. Plots of T 8 against (x + y + z) for structure II (a) and against n (1) and n (2) for structure I!I (b).

shows the relation between Tg and (x + y + z ) for different values of m, i.e. at different branching frequencies, which are determined by the value of 1/m. Here the effect of branching is about the same as in the preceding cases.. However, the appearance of secondary branching leads to a more abrupt increase in the glass transition temperature, which is brought out with special clarity when the branches are short and frequent (m = 0). We will consider branching in the form of a tree. In the case of PE with a trifunctional unit the chemical structure of such a system is represented below . . . . (CHt)--CH . . . .

"

l

i

(CH2)n I

(CH2),~ I

C H - - ( C H z ) n - - C H - - ( C H 2 ) n - - C H _ _ ( ( . . H ~ ) , ~. . . .

(CH-) n

J

(CH2),--CH--(CH~)n--CH

H--ICHt)n--CH--..

I (CH2) n I

....

:

I

1II

In determining ~:ibi it is necessary to allow for the fact that each new branch leads to the necessity of introducing an increment bi and its effect becomes more tangible when the branches are at their shortest. If these branches are of the same length (n = const) then the equation for calculating the glass transition temperature, obtained from (1), takes the form 17.1n + 11.0 Ts = 80.25n - 15.25"

(9)

Effect of branching on polymers

1827

The relation between Tg and n, as calculated from (9), is shown in Fig. 4b. It can easily be seen that when there is branching in the form of a tree, Tg for the system is changed to a much greater extent than in all the previous cases. When the branches become shorter (n = 1), Tg attains 160°C, which is much greater than the value of Tg for the original PE. The reason for such a sharp increase in Tg is that in short branches the chemical structure of the polymer differs significantly from that of PE. Another variant, the branch length distribution, obeys the Flory distribution law. In this case the equation for calculating Tg takes the form i=n K

17.1 ~ i2~2e-iV+ 11.0 i=l

imr/K

80.25 ~ i2~e -iv- 15.25

(10)

i=l

and the results of calculations with (10) are shown in Fig. 4b. It must be noted that when there is a branch length distribution the relation between Tg and n__~is weaker than with branches of the same length; naturally, this comparison was made when n = nw. We will now pass to the consideration of branches of the same chemical nature compared with the main chain, but joined to it through a disjunction of different chemical structure. As an example we will take the structure of the branched polymer represented below, . . . . CHs--CH--(Clts--CHs) m. . . .

(~Hs)n I CHs IV A special case of such a system is an assembly of vinyl esters with different values of n; this corresponds to the case where the value of m = 0. For such a case the equation for calculating Tg takes the form 78.1 + 17. In Tg, K = 289.4 + 80.25n x 103,

(11)

and calculations with (11) lead to the relation between Tg and n given in Fig. 5. This relation is similar to that considered above. Moreover, in the given case the theoretical and experimental results for Tg agree, which is usual with the increments method. When there is a branch length distribution and the branches are arranged randomly along the chain the formula for calculating Ts takes the form i~n K

i=rng

78.1+17.1 ~ i2V2e-iV+ 34.2 ~, j[3e-/~ iEI j=l i-rig

(12)

j'rag

Ts, K = 289.4+80.25 2 i2~e -tv+ 160.5 2 j/3e-/~ i=l i=l In the general case the relation between Tg and the mean number of CH2 groups in the branches

1828

A.A. ASKADSKII and O. V. KOVRIGA

Tg,°C ~0

1.31

0

t,~o

- bO

I

1

3

IO

I, V3

n

FIo. 5. Plots of Ts against n for structure IV (]) and of 7", (2) and no (3) against n for a series of polymethac~lates.

for different values of m appears as shown in Fig. 6. The character of these relations is also similar to that considered above for branched PE. In conclusion we will consider a series of organic glasses based on polymethacrylates. The general formula of such systems has the form CHs I --C H2--CH--

I II 0

C--O--CHz--(CHz)n--CH a

V Since the systems under consideration are transparent materials in the glass-like state, for these it is of interest to determine not only the glass transition temperature but also the refractive index riD, ro. oc

-zo

\

-30

I

3

I

I

3

1

I

I

7

FIo. 6. Plots of Ts against n,~ for structure V.

I

Effect of branching on polymers

1829

and also a series of other characteristics, e.g. the bulk coefficient of thermal expansion in the glass-like state a c , the cohesion energy density (Hildebrand solubility parameter 6), and the surface energy 7. The formula for calculating Tg for this series of branched polymers, as obtained from equation (1), has the form 113.85+ 17.1n T8, K = 355.0 + 80.2n x 103.

(13)

The Hildebrand solubility parameter was calculated from the equation [3]

82= ~'iAEi * NAXiAVi,

(14)

where E~AE~* is the effective cohesion energy, made up of the energy of weak dispersion interaction and strong intermolecular interaction (dipole-dipole, hydrogen bond); XiAVi is the van der Waals volume of a molecule of liquid or a repeating polymer unit; NA is the Avagadro number 82 =

5689 + 646n 0.6023(113.85 + 17. ln)"

(15)

The surface energy was calculated from the equation [5] EiAEi* "Y = Cj (~,~AVi)2/3ml/3 ,

(16)

where m is the number of atoms in a repeating polymer unit, Cj is a factor connected with the molecular packing factor in the bulk of the polymer and on its surface, and depending on the particular class to which the polymer belongs; in our case Cj = 0.0751 [5]. As applied to the series of polymethacrylates under consideration (16) is transformed into the relation (5689 + 646n)4.19 7 = 0.0751 (113.85 + 17. ln) 2j3(18 + 3n)I/3"

(17)

The refractive index was calculated from the equation [3]

no 2 - 1 NAXiAVi nD 2 +

2

kme

= Y-iRi,

(18)

where Y-iRl is the molecular refraction, which is made up of the refraction Ri, inherent in each atom, and from the increments characterizing an additional contribution of the structural features to the refraction (double, triple bonds, aromatic rings, etc.); kme is the mean molecular packing factor for block polymer specimens. In the case of the series of polymethacrylates under consideration equation (18) changes to the equation no 2 - 1 _ (29.362 + 4.618n)0.681 no2+2 0.6023(113.85+ 17.1n)"

(19)

The thermal coefficient of bulk expansion was calculated from the equation [13] ac =

~'iaiA Vi + ~'ifli , ~,i A Vi

(20)

1830

A . A . ASKADSKIIand O. V. KOVRIGA & (collcm3) ~r2 "y,dyne/cm -30

9

- Z6

8

1 5

I .

lll

n

Fio. 7. Plots of 8 (1) and ~,(2) againstn for a seriesof polymethylmethacrylates.

where ai and/3i are the increments associated respectively with the energy of weak dispersion and strong intermolecular interaction. Allowing for the character of the molecular packing fraction as a function of temperature, equation (20), according to [3], can be written in the form a c Tg = 0.0960.

(21)

We used this equation to calculate a o for a series of polymethacrylates having different values of n up to n = 10. Figures 5 and 7 show the calculation results for all the physical characteristics. It can be seen from Fig. 5 that with increase in branch length the glass transition temperature is rapidly decreased, and the refractive index increases. The Hildebrand solubility parameter and the surface energy are inversely related to the branch length (Fig. 7), while the greatest decrease is observed on the initial section of plot of these parameters against n. In the case of this series of polymers, all the calculated characteristics of the physical properties agree with the experimental data quite accurately. In giving the results of these calculations certain conclusions can be arrived at relative to the effect of branching on the physical properties of polymers. The first conclusion is that with increase in branch length the physical properties of polymers are changed only insignificantly and approximate to those of homopolymers of the same chemical structure as the branches themselves. This is true when the branches are located in each repeating unit. If the branches are more rare, and are distributed randomly along the main polymer chain then their effect on the properties is more marked, when their chemical structure differs from that of the main chain. Short branches have the greatest effect on the physical properties. This follows from equations (1), (14), (16), (18), and (21). Thus, for example, in the case of the glass transition temperature the effect of short branches is formally taken into account by the introduction, in the case of each new branch, of the increment bi, in equation (1). This effect is associated with the increase in chain stiffness, and also with the appearance of additional intrermolecular interaction on introduction of a branch containing a polar group. It should also be noted that when there are a large number of short

Synthesis of PA based on anionic polymerization

1831

chain branches the chemical structure of the polymer is changed qualitatively, and if the short chain branches are in the form of a tree, the chemical structure of the system obtained only distantly recalls the chemical structure of the original polymer.

Translated by N. STANDEN REFERENCES 1. A. A. ASKADSKII, Vysokomol. soyed. A31: 10, 2141, 1989 (translated in Polymer Sci. U.S.S.R. 31: 10, 2356, 1989). 2. A. A. ASKADSKII, Vysokomol. soyed. A32: 10, 2149, 1990 (translated in Polymer Sci. U.S.S.R. 32: 10, 2061, 1990). 3. A. A. ASKADSKII and Yu. I. MATEYEV, Khimicheskoe stroenie i fizicheskie svoistva polimerov (Chemical Structure and the Physical Properties of Polymers). Moscow, 1983. 4. L. NILSEN, Mekhanicheskie svoistva polimerov i polimernykh kompositsii (Mechanical Properties of Polymers and Polymer Compositions). Moscow, 1978. 5. A.A. ASKADSKII, M. S. MATEVOSLYANand G. L. SLONIMSKII, Vysokomol. soyed. A29: 4,753, 1987 (translated in Polymer Sci. U.S.S.R. 29: 4,834, 1987).

Polymer Science Vol. 33. No. 9. pp. 1831-1837.1991 Printedin Great Britain.

0965--545X/91$15.00+.00 © 1992PergamonPressLtd

THE SYNTHESIS AND USE OF THREE-DIMENSIONAL STRUCTURE ACTIVATORS BASED ON N-ACRYLOYLCAPROLACTAM IN THE ANIONIC POLYMERIZATION OF CAPROLACTAM* V . V . KURASHEV, V . A . KOTEL'NIKOV, R . B . SHLEIFMAN, S. V . TSUTSURAN, A . A . A S K A D S K i l , V . G . VASIL'YEV, V . V . KAZANTSEVA a n d K . A . BYCHKO A. N. Nesmeyanov Institute for Elemento-Organic Compounds, U.S.S.R. Academy of Sciences (Received 22 October 1990)

A description is given of the synthesis of PA by the anionic polymerization of caprolactam in the presence of new macromolecular polyfunctional activators that promote a three-dimensional structure. PA of this type have a cross-linked structure (gel-fraction in cresol amounts to 100 wt%). The size of the inter-node fragment of the network has been determined as 9850-18500. The PA synthesized are distinguished by a high value of specific impact strength (12-34 kJ/m2 in the Izod test) and are characterized by the existence of hyperelasticity in the temperature range 220-300"C.

THE USE of activators with different chemical natures and functionalities in the anionic polymerization of lactams (APL) opens up wide possibilities for purposefully regulating the molecular structure *Vysokomol. soyed. A33: No. 9, 1956-1961, 1991.