Classes of materials used in medicine - Biomedical Engineering Desk Reference - page 161

O O O O

-C-N CH 2 N-C-O-CH 2 -CH 2 -CH 2 -CH 2 -O- -C-N CH 2 N-C-O- -CH 2 -CH 2 -CH 2 -O —

x y

H H H H

H1 H2 H5 H6 C1 C2 S1 S2 S3

H3 H4

Hard Segment Chain Extender Soft Segment

Carbon Label Shift (ppm)

65
27
71
41
136
129
119
154
165
25

PTMO - CH 2 adjacent to urethane (S1)
PTMO - internal CH 2 (S2)
PTMO - external CH 2 (S3)

MDI CH 2 (H1)

MDI quarternary ring (H2/H5)
MDI protonated ring (H3)
MDI protonated ring (H4)
MDI urethane carbonyl (H6)
BD external CH 2 (C1)
BD external CH 2 (C2)

200 150 100 50 0

Frequency in ppm relative to TMS

Fig. 3.2.2-14 13 C NMR spectrum and peak assignation of a polyurethane [diphenylmethane diisocyanate (MDI, hard segment),
polytetramethylene oxide (PTMO, soft segment), butanediol (BD, chain extender)]. Obtained by cross-polarization magic angle
spinning of the solid polymer. (From Okamoto, D. T., Ph.D. thesis, University of Wisconsin, 1991. Reproduced with permission.)

polymers. Samples are subjected to cyclic deformation at
a fixed frequency in the range of 1-1000 Hz. The stress
response is measured while the cyclic strain is applied
and the temperature is slowly increased (typically at
2-3 degrees/min). If the strain is a sinusoidal function
of time given by:

A typical plot of tan d versus temperature will
display maxima at T g and at lower temperatures where
small-scale motions (secondary relaxations) can occur.
Additional peaks above T g , corresponding to motions in
the crystalline phase and melting, are seen in semi-
crystalline materials. DMA is a sensitive tool for charac-
terizing polymers of similar chemical composition or
for detecting the presence of moderate quantities of
additives.
DSC is another method for probing thermal transi-
tions of polymers. A sample cell and a reference cell are
supplied energy at varying rates so that the temperatures
of the two cells remain equal. The temperature is in-
creased, typically at a rate of 10-20 degrees/min over the
range of interest, and the energy input required to
maintain equality of temperature in the two cells is
recorded. Plots of energy supplied versus average tem-
perature allow determination of T g , crystallization tem-
perature ( T c ), and T m . T g is taken as the temperature at
which one half the change in heat capacity, DC p , has
occurred. The T c and T m are easily identified, as shown in

3 ð u Þ¼ 3 o sin ð u tÞ (3.2.2.7)

where 3 is the time-dependent strain, 3 o is the strain
amplitude, u is the frequency of oscillation, and t is time,
the resulting stress can be expressed by:

s ð u Þ¼ s o sin ð u t þ d Þ (3.2.2.8)

where s is the time-dependent stress, s o is the amplitude
of stress response, and d is the phase angle between stress
and strain. For Hookean solids, the stress and strain are
completely in phase (d ¼ 0), while for purely viscous
liquids, the stress response lags by 90 . Real materials
demonstrate viscoelastic behavior where d has a value
between 0 and 90 .