Macroscopic phenomena in the molecular mobility of polymers under external force fields

Plast. Massy, 2002, No. 10, p. 14-19 Macroscopic phenomena in the molecular mobility of polymers under external force fields Yu.V. Zelenev*, N.N. Peschanskaya** and V.I. Khromov* * The D.I.Mendeleev RKhTU, Moscow ** The A.F.Ioffe Physico-Technical Institute of the Russian Academy of Sciences, St Petersburg Selected from International Polymer Science and Technology, 30, No. 2, 2003, reference PM 02/10/14; transl. serial no. 14941 Translation submitted by J.E. Baker Polymer systems that differ in chemical composition, molecular structure and supramolecular organisation, are characterised by a great variety of mechanisms of thermal motion of kinetic units (relaxation generators) of different types and dimensions, over a wide range of temperatures and frequencies. At sufficiently low temperatures (helium, nitrogen) there is only local mobility of relaxation generators of small masses and dimensions (vibrational, rotational and translational motion of end, side and backbone atomic groups). This is connected with preponderance of the energy of interparticle interactions (effective activation energy U) over the kinetic energy of the thermal motion E k = kt. It should be noted that the local environment of the aforesaid relaxation generators has hardly any influence on the magnitude of U, owing to the fairly large free volume of loosely-packed bulky macromolecules of various classes of polymers (Ref. 1). At higher temperatures, increase in E k gives rise to thermal motion of relaxation generators of larger masses and dimensions (large fragments of chain segments and individual elements of supramolecular structures of the spherulite and fibril type). If for the above reasons we can assume U = const for the local processes of different mechanisms, the restricted nature of the free volume for realisation of mobility of more massive relaxation generators requires a change in the structural environment, i.e. these processes become cooperative, and U will depend both on the external mechanical stress σ, and on the temperature T, i.e. U const. Since nearly all the physical properties of polymers depend on processes of molecular mobility (Ref. 2), it is important to know by what mechanisms the latter is determined and at what temperatures and frequencies of external actions they are manifested, and by what values of U and E k they are characterised. In conditions with action of mechanical fields (both constant and variable) on a polymeric system it is deformed, and its structure changes continuously or in jumps (intermittently) (Ref. 3), at a certain finite rate determined by its chemical composition, molecular structure and supramolecular structure. When the external mechanical stress varies harmonically (σ = σ 0 e iωt ) the shear strain of the polymer will lag behind σ as D = D 0 e i(ωt-δ). In the foregoing δ = E/ E characterises the mechanical losses, E is the energy dissipated per cycle of vibrations, and E is the total energy of the mechanical vibrations. This leads to dissipation of energy during vibration of the specimen, and the polymer will convert the energy of mechanical vibrations to heat. The mechanical losses (internal friction) of a polymer reflect the rearrangement of structural elements within it, occurring at a finite rate. This rearrangement can be of several forms (Ref. 4): thermal (associated with thermal effects), electrical (charge rearrangement), magnetic (magnetomechanical effects), atomic (accompanied by their ordering under stress and redistribution of dislocations by migration) and molecular (limits the relative movement of atomic groups, segments and macromolecules as a whole in the bulk of the polymer). This latter form of rearrangement is currently the least studied, and it is therefore the subject of the present work. The processes of molecular mobility have a significant influence on all the physical properties of polymers and, T/65

in particular, on their static (creep) and dynamic (internal friction) properties, which are manifested over wide temperature-time intervals. In recent years the science of the mechanical properties of polymers has been inseparably linked with molecular relaxation spectrometry. This is because of the results of earlier research into the nature of secondary lowtemperature transitions, measurements of the mechanical losses and of the dynamic elastic modulus, in which the dependence of the dynamic mechanical characteristics on the form of the spectrum of internal friction was noted and discussed (Ref. 5). The subject matter of research work in this country was largely characterised by independence and concerned the not entirely obvious connections between the relaxation regions in the spectra of molecular motions and the statistical limiting strainstrength characteristics. In this article we examine the results of studies for predicting the mechanical properties of solid polymers in various classes (PMMA, PS, PVC, PC, LDPE, ebonite, epoxy resins), as well as polymer films obtained from solutions of powders (PVA, PVA acetals). The polymer samples were in the form of cylinders, 10 and 20 mm long and 2-3 mm in diameter, and films with thickness of 60-100 µm. The results of investigation of the brittle state of glasslike polymers in the little-studied region of low temperatures that is of interest for practical applications and is difficult for predicting the mechanical properties of polymers were presented in earlier works (Refs. 6-13). A number of basic, general rules have now been established, leading to the possibility of predicting the changes in endurance, limit of forced elasticity, kinetic parameters of creep, in some cases the rate of creep, as well as the brittle point of block polymers. In the majority of cases this possibility is based on elucidating the role of molecular motions in formation of the mechanical properties of polymers. Basic rules had previously been established for predicting the endurance of oriented polymers and its kinetic concepts had been formulated. Extensive studies showed that Zhurkov s formula τ = τ 0 exp[(u-ασ)/kt] for endurance reflects the fundamental concepts of the model of fracture of solid polymers and is the most applicable to highly oriented samples. It has been shown (Refs. 6-8) that for amorphous unoriented polymers there is always an admittedly narrow (~50 ) range of temperatures where the straight lines log τ σ form a fan. It should be pointed out that Zhurkov s relation applies to brittle fracture, since the straight lines of endurance form a fan when a polymer fails near the limit of forced elasticity. As the temperature falls and the brittleness increases, polymers display anomalous behaviour, with a number of characteristic features: pronounced dependence of life τ on stress σ, an inverse or weaker dependence of strength on temperature, and kinks on the endurance curves. All these features were called anomalies because they contradicted the existing ideas on the temperature-time relations of polymer strength and could not be explained. We can now call them laws of brittle fracture, which are typical of the brittle state of various types of materials. The variations in the laws predicting endurance are clearer from curves in the coordinates σ b T at log τ = const (Figure 1). In the region of brittle fracture we usually observe 1-2 kinks on these relations, the high-temperature branch of which corresponds to a fan of endurance curves, whereas the low-temperature branches correspond to vertical curves of endurance and a weak temperature dependence. The temperatures of the kinks on the σ b T curve correspond to a jump-like change in creep strain at the moment of fracture, i.e. in some temperature regions (T 1, T 2, T 3 ) there is a sharp change in the motion of the deformational kinetic units (Figure 1). It was logical to compare the regions of the jumps with the regions of relaxation in the spectra of molecular motions (Refs. 7-8). It was found that there is a correspondence between the temperatures of sharp changes in mechanical characteristics and the transitions recorded using NMR (Figure 1). The kinks and turning points on the σ b T and log ε T curves in any case occur at higher temperatures, and are displaced on the temperature scale as a function of specimen life. Temperature-frequency relations for PMMA, constructed from data in the literature, on which points are plotted that correspond to transitions on the mechanical relations for times ~10 3 s (~10-3 Hz), are given in the literature (Ref. 8). Thus, measurement of creep is a method of detecting relaxation transitions corresponding to large time values, and at the same time the temperature variations of the mechanical properties can be predicted from the temperature-frequency curves obtained by another method. For finding the relaxation regions in which changes of mechanical laws can be expected, a more Figure 1. Temperature dependence of the breaking stress σ b (1) at endurance τ = 10 3 s, creep strain (2) at failure for time τ = 10 3 s, and NMR line width H (3) for polyvinyl alcohol. T/66

convenient methodology has now been proposed (Ref. 5) using a laser interferometer for determining the creep rate. With small strains (3 10-4 mm is sufficient), the measurements were effected in the following way. The sample is loaded at the extreme low temperature with a stress σ = 0.1σ B + 20, the strain time diagram is recorded, the sample is unloaded, heated to the next temperature and loaded again with the same stress. The dependence of the creep rate on temperature, determined for identical time and stress, has maxima (Figure 2), i.e. zones with accelerated creep, which correspond to the relaxation transitions (Ref. 5). Simplicity and sensitivity, and good conformity of the relaxation regions to the temperatures of the change in strength characteristics make this variant of the creep method one of the most suitable when studying secondary transitions with the aim of predicting changes in the behaviour of loaded polymers. The rates spectrum (Figure 2) can also be employed for estimating possible regions of viscoelastic transition in polymers. It has been shown (Ref. 3) that the temperature of attaining a level of strain at which necking occurs depends on the type of stress state, but active development of forced-elastic strains (the ductile-brittle transition) gravitates towards the region of the relaxation transition that is nearest in temperature. These considerations contribute considerable definiteness to concepts of the nature of the ductile-brittle transition in polymers and make it easier to predict. The problems of predicting various anomalies of brittle fracture have been examined in a number of works by Shpeizman and Stepanov (Ref. 8). The relaxation model proposed in those works makes it possible to obtain quantitative relations for predicting kinks on the curves of Figure 2. Temperature dependence of creep rate ε (1 - σ = 1 kg/mm 2, 1' - σ = 0.1 kg/mm 2 ) and of breaking stress σ b (2) for endurance of 10 s, for polymethyl methacrylate. endurance, and probability of failure in the case of a vertical time dependence in certain loading conditions, if the activation parameters are known. It is suggested that local stresses, which relax in the region of anomalies at a lower rate, comparable to the rate of fracture itself, are responsible for brittle fracture. Relaxation of local stresses is determined by the rate of local inelastic strain of any kind. The model has been applied for metals and semiconductors, but its assumptions do not contradict concepts on the change in strain capacity of polymers on transition from one relaxation region to another. The problem of predicting dynamic strength during brittle fracture of polymers in the region of inclined time relations is considered in another work (Ref. 7). Data were obtained on the kinetics of crack propagation in PMMA transparent plastic and on dynamic strength for a difficultly-accessible experimental time range (~10-7 s), from which it follows that the breaking stress corresponding to the microsecond range can be estimated by extrapolating the static curve. The inverse dependence of strength, both on temperature and on the loading rate, has to be borne in mind. Sometimes it turns out that these two factors in strength increase (lowering the temperature and increasing the loading rate) lead, on the contrary, to a decrease in strength, owing to the sharp drop in mobility and increase in relaxation time of the structure, which apparently explain unexpected cases of failure of polymer components when their service conditions are changed. The relative position of the static curves of endurance or simply of two strength values for the two boundary values of a wide temperature range can provide information on a polymer s reaction to temperature change and on its susceptibility to embrittlement. There have also been studies of the nature of the variation of the limit of forced elasticity (Ref. 8). It was found that the relations σ B T and σ B log ε cannot be described by a model with one relaxation time, and that molecular rearrangements below T g correspond to changes of the temperature dependence of σ B and the shear modulus G. The relaxation shear modulus was determined from the spectrum of the mechanical losses. Another task undertaken was to describe the temperature and rate dependence of σ B taking into account the spectrum of the relaxation processes (via the shear modulus) and including the molecular dimensions in the characteristics of the elementary event of deformation. Two configurations of the elementary event of inelastic deformation were examined: disclination (bends in long chain molecules) and the dislocation loop, i.e. one of the general mechanisms of inelastic deformation of solids. It was shown for various polymers that best agreement with experiment is observed for the dislocation model (Figure 3). It follows from the literature (Ref. 8) that it is possible to predict the behaviour of glass-like polymers at high stresses over a wide range of experimental conditions from the relaxation characteristics of the linear viscoelastic region. T/67

as a function of temperature, and the transitions on the curves U(T) and α(t) correspond to the transitions on the curves of mechanical property temperature and, accordingly, to the regions of the relaxation transitions, i.e. the spectrum of molecular motions also determines formation of the strain kinetics. One of the most important observations is the slight variation of the U/α ratios throughout the region of the glass-like state. If we express α by the number of monomeric units m in the kinetic unit of creep, we get U/m = U 0 /α/v = q i E coh /3 (2) Figure 3. Temperature dependence of the limit of forced elasticity σ B for polycyclohexyl methacrylate. Dots: experiment; dashed line: calculation based on the dislocation model; solid line: based on a model using dislocation analogies (Ref. 8). Phenomena such as the variation in creep rate over time, special points on the strain and creep curves of polymers, the complex dependence of creep rate on temperature had not, until recently, been the subject of systematic physical investigations. A study of the nature of variation of creep (activation volume and activation energy) when there is a change in strain, temperature, structure and type of stress state (Ref. 8) showed that they are extremely significant for predicting the strain-strength properties of polymers. Systematic studies of the process of creep during compression of various classes of polymers gave unexpected relations, so that certain usual concepts could be examined in a new way. It was shown that the parameters of the activation process of strain (activation energy U, activation volume α and the pre-exponential function ε 0 ), if we take the exponential rate formula U ασ ε = ε 0 exp kt as a conditional description of the essence of the process, vary regularly and identically as a function of strain and temperature (U(ε, T), α(ε, T, ε 0 (ε, T)). The maximum values of the strain parameters correspond to the limit of forced elasticity, and their values are close to those obtained from calculation of the fans log ε σ. Development of forced-elastic strain leads to their decrease to a certain value (1.5-2 times lower than at ε v, which remains constant while the process of flow is in progress). Accordingly, in order to compare U and α with respect to temperature, they must be assigned to a particular strain region. It was found that the kinetic parameters of creep (rate ~10-5 s) exhibit stepwise variation (1) where V is the volume of a monomeric unit, and E coh is the activation energy of viscous flow of the initial monomeric liquid. Using relation (2), it is possible to find q i from the tabulated or calculated value of E coh. Furthermore, q i can easily be found by measuring, just at room temperature by the jump method, the stresses and temperatures of α and U at any point on the creep curve. Next we determine the parameter α(t), which is much easier, in terms of method, than measurement of U 0. Knowing α(t) and q i it is easy to construct the relation U(T) for ε = const from formula (2). When we have the curves α(t) and U(T) we can reduce the number of points on the temperature axis necessary for calculating the preexponential function, using mean rates in experiments for measurement of α in different relaxation regions. After constructing the temperature distribution of the kinetic parameters, it is easy to estimate the creep rate from formula (1) at different temperatures and stresses for an identical region of strains. The estimates are simplified if we find the creep rate for the temperature region between two transitions, where α(t), U(T) and ε 0 change little. It was shown (Ref. 9) that the dislocation model gives good quantitative agreement between the calculated activation volumes α and experiment, i.e. α can be calculated, and the number of experiments can be reduced to a minimum. The established link between the creep characteristics and cohesive energy offers the possibility of estimating the cohesive energy of a monomer, which is methodologically difficult to measure, from mechanical measurements in two experiments (in which we determine α and U) at one temperature on one sample of glass-like polymer. Most of these means of prediction make use of the assumption that the mechanical relations are a function of the relaxation spectrum, and the conformity employed possesses the properties of being fundamental: common to polymers of different classes, manifestation in the most varied characteristics, without contradicting the main concepts of the properties of polymers. On the other hand, it is clear that the possibilities of this approach are by no means exhausted. We can mention several problems whose solution will simplify practical forecasting. T/68

For example, determination of the role of various parameters of the spectrum (height of the peaks of mechanical losses, width of the relaxation zones, temperature interval between transitions); investigation of temperature-frequency relations in different relaxation regions; investigation of the nature and mechanism of relaxation transitions. It follows from the foregoing that secondary relaxation transitions, as well as the high-temperature α-transition, influence the most varied mechanical and kinetic properties of polymers. It must be borne in mind that the existence of relaxation transitions excludes distant extrapolations of properties with respect to temperatures and frequencies (times), i.e. the kinetic relations can be described by an equation with approximately constant parameters within just the given relaxation region. It is to be expected that further development of this promising direction (the connection between the spectrum of molecular motions and mechanical characteristics and relations) will also lead to improved forms of forecasting. For refining the mechanisms of molecular mobility of different classes of polymers, it is interesting to compare the results obtained in mechanical, electric and magnetic fields. Studies in which the processes of molecular mobility in different force fields were investigated in comparable conditions (for the same polymers at identical or similar frequencies and temperature ranges) are the most valuable. Thus, Mikhailov and Kirilina found (Ref. 14) that in measurements at a frequency of 500 Hz, the maxima of the mechanical and dielectric losses of the crosslinked solid polymer ebonite appear at similar temperature values. Similar results were obtained for other polar polymers (Ref. 15) at low strain amplitudes. These results indicate there is a direct connection between the processes of mechanical and electrical relaxation. In a work of one of the authors (Ref. 16), in an investigation of flexiblechain polymers (elastomers) it was shown that for identical materials, with measurement at similar frequencies, the maxima of the dielectric losses appear at higher temperatures, providing evidence of larger effective dimensions of the dielectric relaxation generators (the activation energy corresponding to them is also greater than the mechanical energy: U diel > U mech ). This can be explained by the fact that the electric field acts on the polar groups (side groups, end groups), and through them on the polymer chains. On the other hand, the mechanical field acts directly on parts of the macromolecules ( mechanical relaxation generators ) whose mobility is manifested at temperatures that are not so high (Ref. 17). Similarity of the macroscopic manifestations of the processes of molecular mobility in different force fields occurs for polymers that differ in composition, constitution and structure, and not only in flexibility of the chains and crosslink density in the three-dimensional network. Figure 4 gives the results of investigations of the mechanical and Figure 4. Temperature relations of the dielectric losses tanδ diel (I, IV, VI) and mechanical losses (II, III, V) tanδ mech for high-density polyethylene (a) and polyvinyl chloride (b), obtained in measurements at different frequencies I 5 khz; II 2 MHz; III, IV 300 khz and V, VI 1 khz. dielectric losses of crystalline high-density polyethylene and noncrystalline polyvinyl chloride over a wide temperature range at different frequencies. It can be seen from Figure 4 that the relations tanδ mech (T) and tanδ diel (T) are of almost identical form, but at the same frequencies there is a difference in the temperature position (Figure 4b) of the maxima of the mechanical and dielectric losses. Thus, at a frequency of 2 10 6 Hz the maximum of tanδ mech (T) is 27 below the maximum of tanδ diel (T). At a frequency of 3 10 5 Hz the temperature difference is 11, and at 10 3 Hz it is just 8. On the other hand for ebonite (Ref. 14), which has a dense threedimensional network, at a frequency of 500 Hz this difference is only 3. Such a slight difference suggests that at low strain amplitudes, when only orientational relaxation is manifested, mechanical and electrical relaxation have common mechanisms. The mechanical and dielectric losses in different polymers are then determined by the same form of thermal motion. This is confirmed by coincidence of the corresponding values of activation energy and the most-probable relaxation times. For sufficiently high frequencies (10 4 Hz and above) the magnitude of the maximum of the dielectric losses is greater than for the mechanical losses, and vice versa for frequencies below 10 4 Hz. The opposite character of the variation in level of the maxima of tanδ mech and tanδ diel on variation of frequency is due to the fact that the magnitude of the maximum of the dielectric losses is determined by the polarity of the side groups or radicals, whereas the level of the maxima of the mechanical losses is determined by their mass. It is the value of the polarity of the polymers (the magnitude of the effective dipole moment µ eff of these groups) that determines not only the level, but also the temperature position of the T/69

maxima of the dielectric losses. With increase in µ eff the maximum of tanδ diel is shifted towards higher temperatures, which corresponds to a decrease in mobility of these groups with increase in polarity of the polymers. The influence of the length of radicals that are bound chemically to the main chains, at similar values of µ eff, is manifested as a shift of the maxima of tanδ diel (T) to the low-temperature region as their dimensions increase, indicating that their mobility is facilitated. Molecular relaxation of polymers, occurring both in electric and in mechanical fields, can be divided into two main types: strictly relaxation of polymer groups (or radicals) and relaxation of these groups together with the adjacent sections of the main chains. These (complex) larger relaxation generators are generally called segments. They exist in various classes of polymers: linear, branched, crosslinked, containing cycles in the chains, as well as in amorphous and partially crystalline polymers. Dielectric losses of the first type are generally called dipole-group (radical) losses, and those of the second type are called dipole-segmental losses (elastic, because transition of polymers from the glassy to the highly elastic state is associated with unfreezing of the mobility of chain segments, the dimensions of which are determined by the chemical composition of the polymers). Molecular mobility of the first type is usually manifested at low temperatures or high frequencies, and of the second type at high temperatures and low frequencies. However, dipolegroup losses are not a characteristic feature of the glassy state of polymers, but may also occur in their highly elastic state, if the period of the applied alternating electric field is comparable to the relaxation time of the given type of losses at temperature T > T g. (T g is the temperature of transition of the polymer from the glassy state to the highly elastic state). Consequently, the dipole-group losses also reflect the processes of molecular relaxation, which are caused by the motion of polar side groups in conditions when the main chains remain immobile for a time that is comparable to the period of the oscillations of the applied electric field. If this period is large enough, at certain temperatures we may observe dipole-segmental losses, which are caused by mobility of fairly large regions of the chains (segments) together with polar side groups. It should be pointed out that the temperature-frequency position of the maximum of tanδ diel of the dipole-group losses does not depend on the presence of low-molecular impurities, whereas for dipole-segmental losses it is strongly dependent, which is manifested in shorter relaxation times of the corresponding process. Crosslinking of macromolecules, which hampers their mobility and increases the relaxation times of dipolesegmental processes, has the opposite effect. Stretching of polymers, leading to orientation of the main chains, increases the relaxation times of the dipolesegmental processes, but has no effect on the relaxation times of the dipole-group processes. Both forms of dielectric losses are greatly affected by change in the chemical composition and structure of the monomeric unit of the polymer chain, and by atomic groups (polar and nonpolar) attached both directly to the main chain, and to lateral appendages (groups, radicals). In a comparative study of dielectric and mechanical losses it was established (Ref. 18) that replacement of a nonpolar methyl group in the α position in polymethyl methacrylate with the polar group CCl, which is of the same volume, causes significant slowing of the segmental motion of the macromolecules. Moreover, the effect of polarity can be intensified if the CH 3 group is replaced with the CN group, with a dipole moment µ eff = 3.4 D that is even larger than for CCl (µ eff = 1.9 D). A comparative investigation of the temperature relations tanδ mech (T) and tanδ diel (T) for HDPE gives grounds for believing that the low-temperature maximum β is caused by the development of mobility of segments of the main chains, consisting of four methylene groups CH 2, whereas the high-temperature α maximum is connected with incipient fusion of poorly formed crystals. Investigations of low-density polyethylene (LDPE), which is far more branched and has lower density and crystallinity, showed that the dielectric loss method has its limitations. In particular, it does not permit observation of the γ maximum, which is clearly identified by the mechanical loss method (Figure 5). According to data in the literature (Ref. 18) it is connected with mobility of individual CH 2 groups located in side branches (the amorphous parts of LDPE). Figure 5. Temperature relations of mechanical losses (I, IV), Young s modulus E (II), width of the NMR absorption line (III, VI), shear modulus G (V) for high-pressure (low-density) polyethylene (a) and polyvinyl chloride (b), obtained at different frequencies: I, II 1 khz; IV, V 1 Hz. T/70

A valuable supplement to the mechanical loss method when studying molecular motions is NMR spectroscopy (broad line method or pulse method). In particular it makes it possible to observe rotation about groups of linkages in polymer chains (Ref. 19). Application of NMR for investigating the molecular mobility of polymers is based on measurement of the function of line width H, which becomes much narrower (monotonically or in steps) as the temperature rises and thermal motion is intensified. This method of investigating polymers in magnetic fields makes it possible to determine both the nature of the mobility of groups, and the character and rate of their motion. A comparative examination of the results of investigation of partially crystalline LDPE and noncrystalline polyvinyl chloride provided additional information on their molecular mobility. It follows from the data in Figure 5 that the width H of the NMR absorption line varies with temperature similarly to the shear modulus G. In the temperature range 350-360 K, corresponding to the glass-transition/softening range, there is a sharp change in the values of H, G and tanδ mech. A sharp change in H also occurs in the transformation temperature ranges of polymers, observable in refractometric measurements and measurements of heat capacity (Ref. 20). The existence of a correlation between these data means we can link the sharp change in H in this temperature range to the start of motion of segments of the polymer chains. For the γ and α peaks of the mechanical losses of polyvinyl chloride, no such correlation with change in H is observed, indicating the limitations of NMR for these studies and that it cannot be used for interpreting all mechanisms of molecular mobility in polymers. The appearance of a γ maximum for LDPE on the relation tanδ mech (T) may be connected with transverse vibrations of CH 2 groups present in the branchings of the amorphous part of the polymer. The β maximum in the relation tanδ mech (T) for LDPE may be connected with rotations of the CH 2 side groups, and the α maximum may be caused by unfreezing of the segmental mobility in LDPE. On the basis of calculation of the values of the second moment of the NMR lines of H 2 2 the γ maximum can be linked to reorientation of CH 2 groups (Ref. 21). It is suggested in another work (Ref. 22) that the γ peak may be due to a change in the nature of stereoregularity as a result of cooperative trans-cis transitions in the macromolecules. For polyvinyl chloride, the broad, gently-sloping maximum at 225 K is due to the mobility of CCl side appendages, and the high-temperature maximum at 365 K is connected with the appearance of segmental mobility. 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