Thermal expansion of glassy polymers

1043

Thermal expansion of glassy polymers K.W.M. Daw and M. Braden Dental School of the”Royal London Hospital Medical College IRC for Biomedical Materials, University of London, Turner Street, London El 2AD, UK The thermal expansion of a number of glassy polymers of interest in dentistry has been studied using a quartz dilatometer. In some cases, the expansion was linear and therefore the coefficient of thermal expansion readily determined. Other polymers exhibited non-linear behaviour and values appropriate to different temperature ranges are quoted. The linear coefficient of thermal expansion was, to a first approximation, a function of both the molar volume and van der Waal’s volume of the repeating unit. Keywords:

Dental materials,

glassy polymers,

thermal

expansion

Received 12 December 1991; revised 28 January 1992; accepted 20 March 1992

The coefficient of thermal expansion of polymers used in dentistry is of major importance, because restorative materials should ideally match the tooth in this respect. Polymers in general have a high coefficient of thermal expansion and indeed one major reason for the development of composite filling materials was to reduce thermal expansion. Clearly, however, the selection of polymers with as low a coefficient as possible would be desirable. This subject seems to have received scant attention in the dental literature, although there is a considerable body of published literature in the subject per se [see below). In this work, a wide range of methacrylate structure types have been studied in an attempt to find if there is any general correlation with structure.

MATERIALS

AND METHODS

Materials The monomers used to synthesize homopolymers are listed in Table2. The following synthetic routes were used for monomers that were not commercially available: 1. Transesterification For the preparation of: isopropyl methacrylate benzyl methacrylate 3 phenyl propyl methacrylate 2. Reaction of the sodium salt of methacrylic monochloroacetone For the preparation of: 2-oxopropyl methacrylate Correspondence

to Dr K.W.M.

@ 1992 Butterworth-Heinemann 0142-9612/92/141043-04

Ltd

Davy.

acid with

3. Reaction

of glycidyl methacrylate with: (a) monocarboxylic and dicarboxylic acids For the preparation of: 3 methacryloyloxy-2-hydroxypropyl benzoate 3 methacryloyloxy-2-hydroxypropyl-(%methylbenzoate) 3 methacryloyloxy-2-hydroxypropyl-[3-methylbenzoate) 3 methacryloyloxy-2-hydroxypropyl-(4-t-butyl benzoate) 2-hydroxypropyl-l-3-dimethacrylate bis(2-hydroxy-3-methacryloyloxypropyl)benzene1,2_dicarboxylate bis(2-hydroxy-3-methacryloyloxypropyl)benzene-l,3dicarboxylate bis(2-hydroxy-3-methacryloyloxypropyl)-3-nitrobenzene-1,2_dicarboxylate (b) phenols For the preparation of: l-phenoxy-2-hydroxypropyl methacrylate 1-(4methyl phenoxy)-2-hydroxypropyl methacrylate

We also studied the polymer of dioctyl tin dimethacrylate, supplied by the International Tin Research Institute. This wide range of polymers was studied in an effort to discern any correlation with structure. Homopolymers were made by first incorporating 1% benzoyl peroxide as 2% Lucid01 CH50, a benzoyl peroxide/dicyclohexyl phthalate master batch. Cylindrical samples were made in a three part Teflon@ mould by introducing the monomer into the mould, which was then closed, and put under a pressure of 0.3 MPa in a pressure cooker and cured overnight at 80°C. This method gave samples free of air bubbles. The sample had nominal dimensions of 7 X 1 cm diameter. This was subsequently this removed reduced to -5 X 0.5 cm by grinding; Biomaterials

1992, Vol. 13 No. 14

1044

Thermal

Table 1

Monomers

Methacrylate

of glassy polymers:

K. WM.

Davy and M. Braden

used to synthesize homopolymers

ester

Methyl Ethyl Propyl n-butyl lsobutyl lsoheptyl Cyclohexyl 2-hydroxyethyl P-hydroxypropyl 3-hydroxypropyl Glycidyl 2-oxopropyl Benzyl 3-phenyl propyl Furfuryl 2-hydroxypropyl-benzoate 2-hydroxypropyl (a-methyl benzoate) 2-hydroxypropyl (3-methyl benzoate) 2-hydroxypropyl-~4-t butyl benzoate) I-phenoxy-2-hydroxypropyl 1(4-methyl phenoxy) P-hydroxypropyl Dimethacrylate esters Ethylene glycol 2-hydroxypropyl Triethylene glycol Tetraethylene glycol 1,bButane diol Methac~loyloxyphthalate esters bis(2-hydroxy-3-methacryloyloxypropyl) benzene1,2-dicarboxylate bis(2-hydroxy-3-methacryloyloxypropyl) benzene1,&dicarboxylate bis(2-hydroxy-3-methacryloyloxypropyl)-3nitrobenzene-1,2dicarboxylate bis GMA esters bis-GMA dimethacrylatea Ethoxylated - bis-GMA dimethacrylateb Propoxylated - bis-GMA dimethacrylateC lsopropoxylated - bis-GMA dimethacrylated ‘2,2-bis b2,2-bis ‘2,2-bis d2,2-bis

expansion

Molecular mass

Density g/cm3

Molar volume cm3/mole (Ve)

van der Waal’s volume cm3/mo/e (V,)

100 114 126 142 142 185 168 130 144 144 142 142 176 204 152 264 278

1.1880 1.1190 1.0996 1.0550 1.0520 1.0124 1.1146 1.2487 1.2100 1.2144 1.2792 1.2467 1.1867 1.1532 1.2653 1.2866 1.2622

86.50 102.40 118.20 134.10 135.70 191.30 151.30 104.00 121.50 119.85 113.75 116.95 151.15 182.85 120.10 208.95 225.85

56.10 66.33 76.56 86.79 86.79 120.92 99.23 70.93 81.00 81 .OO 74.87 78.00 101.50 121.96 81.53 138.76 152.42

278

1.2558

225.85

152.42

320

1.1749

278.25

236 250

1.2595 1.2287

198 228 286 330 226

Coefficient of thermal expansion (P) K-l X lo5

p vg x 10-Z

7.31 9.23 12.20 12.30 10.20 12.20 7.54 8.94 6.06 4.65 10.52 7.74 8.31 8.59 7.35 7.39 6.73

0.63 0.95 1.44 1.65 1.38 2.33 1.14 0.93 0.74 0.56 1.20 0.91 1.26 1.57 0.78 1.54 1.52

(5.85)

9.16

2.07

183.09

(6.36)

10.29

2.86

196.15 212.85

127.25 140.92

;::q

8.23 7.10

1.61 1.51

1.2477 1.3001 1.2468 1.2473 1.2079

156.90 176.05 240.30 282.00 188.60

105.15 120.08 153.47 177.67 125.61

I::::; (6.40) (8.41) (6.60)

7.25 5.96 8.11 10.00 7.92

1.14 1.05 1.95 2.82 1.49

450

1.3163

338.40

215.44

(5.39)

8.16

2.76

450

1.3135

338.40

215.44

(5.91)

8.64

2.92

495

1.3438

368.30

250.98

(6.46)

10.40

3.83

512 452

1.2370 1.2051

430.30 392.00

280.13 250.49

(4.32) (4.59)

8.29 6.38

3.56 2.50

480

1.1815

423.70

270.95

(5.96)

6.74

2.86

480

1.1644

427.00

270.93

(4.68)

6.44

2.75

(9.23) (6.62) (5.89) (4.55) (8.18) I::!;; (5.4)

4- 3-methac~loylo~(Z-hydroxypropyl) phenyl propane. 4(2-methac~loyloxyethoxy) phenyi propane. 4(3-methacryloyloxypropoxy) phenyl propane. 4(2-methacryloyloxypropoxy) phenyl propane.

surface stickiness due to air inhibition. The overall length of the specimen was measured at room temperature with Vernier callipers to 2~0.01 cm. The prepared sample was placed in a quartz dilatometer and a quartz rod and dial gauge assembly engaged with the top of the sample. The whole assembly was placed in a thermostat bath, capable of temperature control +O.l”C in the range --25’C to 50’C and the temperature reduced to -25’C, and then raised to -20°C and the dial gauge zeroed. A series of dilatometer readings were taken at 2°C intervals, Ieaving at ieast 30 min before each reading. Biomaterials

1992,

Vol.

13 No. 14

Expansion versus temperature was plotted to give the coefficient of thermal expansion. Density of polymers was determined separately by hydrostatic weighing.

RESULTS Figures 1 and 2 give two typical traces. In Figure 2, where the graph is linear over the range studied, there is no ambiguity over the coefficient of thermal expansion.

Thermal

expansion

1045

K. W.M. Davy and M. Braden

of glassy polymers:

Table 2 Values of the linear coefficient of thermal expansion from van Krevelen

.J

a

0.1

Polymer

/3(K-’ x 104)

Poly(methyl methacrylate) Poly(ethyl methacrylate) Poly(propyl methacrylate) Poly(isobutyl methacrylate)

0.90 1.04 1.14 0.76-0.87

Waal’s volume. Table 2 lists some data obtained from the literature, for comparison purposes’. These were calculated from data in van Krevelen’, from:

-

p = pE,‘3M wherep

= density,

E = (av/dT], M = molecular

weight.

DISCUSSION The data in Table I indicate a range of 4.32-12.3 X low5 K-’ where available, the data obtained in this work are in reasonable agreement with published data, considering the sources of error discussed above. The question arises whether there is any correlation with structure and which attribuie influences thermal expansion Van Krevelen2, a definitive text on the subject, has suggested that the molar thermal expansivity (E,) is related to the van der Waal’s volume of the repeating unit of the polymer by the relationship:

I

0

-20

20 OC

Figure 1

Expansion curve for poly(jsobu~i

methacrylate).

0.2 k

% - 4.5 x 1o-4 v,

(2)

where EB and V, refers to the amorphous

glassy state:

P

V, being the molar volume

-20

0

20

of the repeating unit. The van der Waal’s volume, VW is defined by Bondi as ‘the volume occupied by a molecule that is impenetrable for other molecules with thermal energies at ordinary temperatures’. Bondi deduced such values on the basis of X-ray diffraction data, gas kinetic collision crosssection, critical density and liquid state properties. The values were correlated with atomic radii obtained from the de Broglie wavelength of the outermost electron. Hence van der Waal’s volumes for a number of chemical moities were obtained (Table 2). These can be used to calculate VW for all the monomers studied. Since the value coefficient of expansion can be written as:

40

OC

Figure 2 Expansion curve for bis(Z-hydroxy-3-methac~ioyloxypropytf benzene-1,2-dicarboxyfate.

and the linear 1T =

I,[1 + PO-- T,ll

(11

However, where there is a discontinuity, with two linear regions, two coefficients are quoted. Clearly for dental applications, the higher one is relevant. Variation of p with temperature has been observed for a number of methacrylates’. Table 3 lists the linear coefficients of thermal expansion, together with data on density, molar volume and van der

3 pv,

coefficient

is p = a/3, it follows

that:

= 4.5 x 1o-4 v,

*‘. p v, = 1.5 x 10-4 v,

(51

Figure 3 plots @VP versus V,,, from the data in Table 1 and the full line is for a slope of 1.5 X 10S4; there is reasonable correspondence of the data to the theoretical line, albeit with much scatter and most points lie below the line. The correlation coefficient is 0.582, with 33” of freedom: this is highly significant withp << 0.01. There is Biomaterials

1992, Vol. 13 No. 14

1046

Thermal

expansion

of glassy polymers:

K. W.M. Davy and M. Braden

predicts all glassy polymers to have a linear coefficient of thermal expansion of 9.7 X lop5 K-‘. Clearly this is not the case, although some materials approximate to this. The reason for this becomes clear when the values of V,l V, are considered (Table 2); these are in the range 0.630.69, hence the value of V,/V, will vary to some extent according to the actual chemical groups present. Hence there is some very limited scope in the selection of molecular structures for low thermal expansion: sulphur for example is a good candidate atom in this respect.

CONCLUSIONS

I

100 V

I

I

200

300

The determination of linear coefficient of thermal expansion (p) of a wide range of methacrylate polymers gives a range of 4.32-15.8 X 1O-5 K-‘. The data correspond reasonably with the theoretical relationship V, = 1.5 X lop4 VW; if V,/V, is assumed to be 0.65 as a wide body of data suggests, all glassy polymers shouid have a value of 9.7 X 10U5 K-‘. The wider range of values obtained is a consequence of VJVs varying for various chemical groupings around the 0.65 value and the difficulty of ascribing an exact value to p, where thermal expansion is not linear with temperature.

w

Figure3 Plot of p Vg versus VW. /3 = linear coefficient of thermal expansion; V, = molar volume of repeating unit in polymer; VW= van der Waal’s volume.

REFERENCES 1

a further rewritten:

implication

of Equation

5 which

can

be 2

p = 1.5 x 1o-4 VW/V,

Estimation

(6)

Van Kreveler? has shown that to a good first approximation V, is a linear function of Vs with V, = 0.65 Vs; this

Biomaterials

1992. Vol. 13 No. 14

Haldon, R. and Simha, R., Multiple transitions inpolyalkyl methacrylates, J Appl. Phys. 1968,39,1890-1899 van Krevelen, D.W., Properties of Polymers - Their

3

and Correlation

With Chemical

Structure,

Chapter 4, Volumetric properties, Elsevier, Amsterdam, Oxford, New York, 1976,pp 67-74 Bondi, A., van der Waal’s volumes and radii, J. Physics. Chem. 1964,66.441-451