The glassy state

In the amorphous state, the distribution of polymer chains in the matrix is completely random, with none of the strictures imposed by the ordering encoimtered in the crystallites of partially crystalline polymers. This allows the onset of molecular motion in amorphous polymers to take place at temperatures below the melting point of such crystallites. Consequently, as the molecular motion in an amorphous polymer increases, the sample passes from a glass through a rubberhke state imtil finally it becomes molten. These transitions lead to changes in the physical properties and material application of a polymer, and it is important to examine physical changes wrought in an amorphous polymer as a result of variations in the molecular motion. 

Polymers do not form perfectly elastic solids, as a limited amount of bond rotation can occur in the glass, which allows slight plastic deformation this makes them somewhat tougher than inorganic glass. 

The molecular mechanisms for a number of these subglass transition relaxations have now been established, often by relating the temperature dependence of the frequency of the observed mechanical or dielectric relaxations to specific molecular motions, identified using either experiments (e.g., NMR and neutron scattering) or, more recently, computer simulations. By way of illustration, some examples of group motions that have been found to be active in a series of poly(alkyl methacrylate)s will be described in the following text. 

FIGURE 12.1 Schematic representation of the Boyer crankshaft motion. 

As these relaxations require energy and arc associated with a characteristic activation eneigy, it has bear suggested that they may improve the impact resistance of some materials. This point still requires confirmation as a general phenomenon, but there is litfle doubt that polymer molecules are not totally frozen or immobile when in the glassy state, and that small subunits in the chain can remain mechanically and dielectrically active below T.  

Continuous ribbons can be obtained at speeds of the order of 1 Rm/minute. Molten alloys can be injected into the space between spring loaded and cooled rollers spinning in opposite directions. Removal of heat in such a set-up is even better than when a single roller is employed because of the effective use of both the surfaces of the ribbon. Methods have also been developed where drops (instead of jets) of the liquid are 

Sol-gel process (Ganguli, 1989 Brinker and Scherer, 1990) is another important method of preparation of glasses. Sol-gel method is essentially a chimie-douce process. A sol by definition is a suspension of colloidal particles, which are of submicron or nanometric size. If these particles have surface active groups such as hydroxyls, interparticle connections are established by a condensation reaction. If the condensation occurs in such as way that the condensation product namely H2O, or the solvent is locked up in the matrix of sol particles, a mildly rigid product is formed, which is known as a gel. A colloidal particle formation can be an intermediate stage and it is not necessary to start with a colloidal suspension only. For example, when sodium silicate is dissolved in H2O, it is hydrolyzed to give silicic acid which forms a gel. Si(OH)4 molecules condense to form Si-O-Si linkages as follows  

Since the key to gelation is the formation of extensive M-O-M linkages, it can be brought about by the controlled hydrolysis of metalorganics. For example, tetra-ethoxy silane (TEOS) is a metal organic, soluble in ethanol. This solution can be kept stirred with continuous and slow addition of H2O, which brings about the following reactions, 

The amorphous state, therefore, can be arrived at by methods other than melting and quenching and all such methods result in the loss of crystalline order. All these processes introduce additional enthalpy into the disordered material. Therefore amorphous materials crystallize irreversibly when heated to a temperature. Ter below of the parent crystalline material and the process is exothermic. The free energy of the amorphous state of a material is higher than that of its crystalline state. Thus the enthalpy addition (A//) during amorphization has to be generally 

Sulfides AS2S3, Sb2S3 and various sulfides of B, Ga, In, Tc, Gc, Sn, N, P, Bi. CS21 Li2S-B2S3, P2S5 Li2S etc. 

At temperatures below r , the material is in glassy state and only small increases in free volume due to molecular motions can modify the moduli F is slightly decreased along with small increases in F. In this region, w t3 1 that is, the applied oscillatory deformation is faster than the relaxation time of the side-group polymer segments, and consequently the material shows a rigid behavior. 

In this range, small peaks can appear in the loss modulus evolution these peaks are associated with secondary transitions in the glassy-state, referred to as 

The differences between the values of viscosity, rj, and liquid surface energy, ctlv, of metals and glasses are of importance because the ratio orv/ 1 is of major significance in determining spreading rates (see equation (2.4)) and flow rates in capillaries (see equation (10.1)). For glassy materials, the ratio is less, and 

T omsia 1981). Similarly, the presence of MnO in the glass seems to be the cause of the almost perfect wetting of Pt by MnO-30SiO2, Table 9.2. 

(1970) Surface Tensions of Molten Salts and Contact Angle Measurements of Molten Salts on Solids, EUR 4482 e, Commission of the European Communities-Euratom, Joint Nuclear Research Centre, Petten Establishment, Netherlands Nicholas, M. G. (1986a)7. Mater. Sci., 21, 3392 Nicholas, M. G. (1986b) Brit. Ceram. Trans., 85, 144 

Weinrauch, D. A. and Lazaroff, J. E. (1995) in Proc. Int. Conf. High Temperature Capillarity, Smolenice Castle, May 1994, ed. N. Eustathopoulos (Reproprint, Bratislava) p. 330 

andTomsia, A. P. (1981) in Surfaces and Interfaces in Ceramic and Ceramic-Metal Systems, ed. J. A. Pask and A. G. Evans, Plenum Press, New York, p. 411 Pask, J. A. (1987) Ceram. Bull., 66, 1587 Pask, J. A. (1993) J. Materials Synthesis and Processing, 1,125 

It has been mentioned in several previous chapters that below the glass transition temperature the convolutions of polymer chain backbones are largely immobilized. Thus, most viscoelastic properties in the glassy state must reflect limited local molecular motions. There are several possible types of these torsional oscillations, rotations around chain backbone bonds with short-range coordination, various configurational rearrangements of side chains, and rotations of terminal groups of side chains such as methyl which require very little cooperation from the environment. 

Molecular motions very similar to some of these may also occur in vitrifying liquids of low molecular weight near and below Tg. Indeed, the bulk viscoelastic properties, as evidenced by the course of volume contraction near Tg illustrated in Fig. 11 -7 and discussed further in Chapter 18, seem to be very similar for both polymers and small molecules (Section B1 of Chapter 18). In shear viscoelastic properties, however, there are some characteristic differences, and it is instructive to examine the behavior of small molecules first. 

AMORPHOUS SOUDS AND SUPERCOOLED LIQUIDS OF LOW MOLECULAR WEIGHT 

At high frequencies, however, there is a transition (abrupt in the hydroxypen- 

Loss tangent plotted against frequency for three glasses of low molecular weight and two polymeric glasses. (HPF) Hydroxypentamethyl flavan (GSP) glycerol sextol phthalate (I) 2-phe-nyl-3-p-tolylindanone (PMM) polymethyl methacrylate (calculated from data of Lethersich ) (PS) polystyrene. (After Benbow and Wood. ) 

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At very short times the modulus is on the order of 10" ° N m comparable to ordinary window glass at room temperature. In fact, the mechanical behavior displayed in this region is called the glassy state, regardless of the chemical composition of the specimen. Inorganic and polymeric glasses... 

At very short times the compliance is low and essentially constant. This is the glassy state where chain motion requires longer times to be observed. 

At longer times an increase in compliance marks the relaxation of the glassy state to the rubbery state. Again, an increase of temperature through Tg would produce the same effect. 

A variety of experimental techniques have been employed to research the material of this chapter, many of which we shall not even mention. For example, pressure as well as temperature has been used as an experimental variable to study volume effects. Dielectric constants, indices of refraction, and nuclear magnetic resonsance (NMR) spectra are used, as well as mechanical relaxations, to monitor the onset of the glassy state. X-ray, electron, and neutron diffraction are used to elucidate structure along with electron microscopy. It would take us too far afield to trace all these different techniques and the results obtained from each, so we restrict ourselves to discussing only a few types of experimental data. Our failure to mention all sources of data does not imply that these other techniques have not been employed to good advantage in the study of the topics contained herein. 

New photochromic dyes with electrocycHc reactions have been proposed on the basis of 1,5-electtocycHzation of heterogenous pentadienyl—anions (124). StiH newer are investigations into the photocycHzation of 2,4,6-tri-isoptopylbenzophenones for vinyl polymers ia the glassy state (133). 

In the preparation and processing of ionomers, plasticizers may be added to reduce viscosity at elevated temperatures and to permit easier processing. These plasticizers have an effect, as well, on the mechanical properties, both in the rubbery state and in the glassy state these effects depend on the composition of the ionomer, the polar or nonpolar nature of the plasticizer and on the concentration. Many studies have been carried out on plasticized ionomers and on the influence of plasticizer on viscoelastic and relaxation behavior and a review of this subject has been given 119]. However, there is still relatively little information on effects of plasticizer type and concentration on specific mechanical properties of ionomers in the glassy state or solid state. 

PMMA ionomers in the glassy state than does the nonpolar DOP. 

There are other conditions that result from the frozen-in stresses. In materials such as crystal polystyrene, which have low elongation to fracture and are in the glassy state at room temperature, a frequent result is crazing it is the appearance of many fine microcracks across the material in a direction perpendicular to the stress direction. This result may not appear immediately and may occur by exposure to either a mildly solvent liquid or vapor. Styrene products dipped in kerosene will craze quickly in stressed areas. 

There is another result of frozen-in residual stresses that can be equally damaging to the product function and which affects materials that are not in the glassy state. This may affect an impact grade of material or a crystalline plastic even more drastically than a glassy material. The frozen-in stresses are real loads applied to the material and when even slightly elevated temperatures are applied stresses can cause the product to deform severely. 

The glassy state does not represent a true equilibrium phase. Below the transition into a glass phase, the material is regarded as being in a metastable state. If one holds the substances at temperatures somewhat below the glass transition temperature, heat evolution can often be observed over time as the molecules slowly orient themselves into the lower energy, stable crystalline phase. 

A similar mechanoehemieal chain reaction was proposed to explain the microcrack formation in the glassy state [143] ... 

Molecular Motion in amorphous atactic polystyrene (PS) is more complicated and a number of relaxation processes, a through 5 have been detected by various techniques as reviewed recently by Sillescu74). Of course, motions above and below the glass transition temperature Tg have to be treated separately, as well as chain and side group mobility, respectively. Motion well above Tg as well as phenyl motion in the glassy state, involving rapid 180° jumps around their axes to the backbone has been discussed in detail in Ref.17). Here we will concentrate on chain mobility in the vicinity of the glass transition. 

Polycarbonate (PC) serves as a convenient example for both, the direct determination of the distribution of correlation times and the close connection of localized motions and mechanical properties. This material shows a pronounced P-relaxation in the glassy state, but the nature of the corresponding motional mechanism was not clear 76 80> before the advent of advanced NMR techniques. Meanwhile it has been shown both from 2H NMR 17) and later from 13C NMRSI) that only the phenyl groups exhibit major mobility, consisting in 180° flips augmented by substantial small angle fluctuations about the same axis, reaching an rms amplitude of 35° at 380 K, for details see Ref. 17). 

Fig. 29. Observed and calculated 2H NMR spectra for the mesogenic groups of a) the nematic (m = 2), b) the smectic (m = 6) liquid crystalline polymer in the glassy state, showing the line shape changes due to the freezing of the jump motion of the labelled phenyl ring. The exchange frequency corresponds to the centre of the distribution of correlation times. Note that the order parameters are different, S = 0.65 in the frozen nematic, and S = 0.85 in the frozen smectic system, respectively...

Such considerations appear to be very relevant to the deformation of polymethylmethacrylate (PMMA) in the glassy state. At first sight, the development of P200 with draw ratio appears to follow the pseudo-affine deformation scheme rather than the rubber network model. It is, however, not possible to reconcile this conclusion with the temperature dependence of the behaviour where the development of orientation reduces in absolute magnitude with increasing temperature of deformation. It was proposed by Raha and Bowden 25) that an alternative deformation scheme, which fits the data well, is to assume that the deformation is akin to a rubber network, where the number of cross-links systematically reduces as the draw ratio is increased. It is assumed that the reduction in the number of cross-links per unit volume N i.e. molecular entanglements is proportional to the degree of deformation. 

In the uniaxially oriented sheets of PET, it has been concluded that the Young s modulus in the draw direction does not correlate with the amorphous orientation fa or with xa "VP2(0)> 1r as might have been expected on the Prevorsek model37). There is, however, an excellent correlation between the modulus and x,rans,rans as shown in Fig. 15. It has therefore been concluded 29) that the modulus in drawn PET depends primarily on the molecular chains which are in the extended trans conformation, irrespective of whether these chains are in a crystalline or amorphous environment. It appears that in the glassy state such trans sequences could act to reinforce the structure much as fibres in a fibre composite. 

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