Structure-property relationships--linear and star-branched macrostructures.

Solution anionic polymerization is perhaps the most useful loot for the synthesis of polymer molecules with well-defined structure. The inherent stability of the anionic propagating center allows for a level of polymerization control unrivaled by other commercially significant polymerization systems. The term macrostructure is used to describe the architectural features of the polymer chain, including molecular weight, molecular weight distribution and extent and type of branching (ref. 1). Branch sites along a polymer backbone can be either short chain (comb-like) structures, long chain branching, simple star structures derived from linking reactions, or highly branched dendritic structures (ref. 2). Often the nature and extent of branching and the breadth of the molecular weight distribution are dependent on the catalyst or initiating system and polymerization conditions. By controlling the macrostructure, the rheological properties of an elastomeric product can be dictated.

Defining structure-property relationships between the polymer macrostructure and the rheological behavior of the product is the key to developing diene-based elastomer systems for the robber industry, especially the tire industry (ref. 3). The microstructure of an amorphous elastomer is the critical design consideration when establishing the utility of a product for a certain application in terms of cure kinetics, wet and dry tire traction, and abrasion resistance. However, the macrostructure of the polymer is the most important feature when considering the hysteretic behavior of the product, and, most importantly, the processing characteristics.

The production of filled rubber goods is processing-intensive, with several stages of internal mixing, calendering and extrusion typical for component preparation (ref. 4). Therefore, controlling and measuring a raw elastomer's theological behavior is crucial. Commercial producers of anionic diene-based elastomers have developed several chemical and polymerization process technologies to tightly control the macrostructure of their products over a wide range of microstructures. While highly linear chains of narrow polydispersity are desirable for low hysteresis, branched macrostructures offer benefits in processing. In general, higher molecular weight polymers are less hysteretic because there are fewer elastically ineffective chain ends (refs. 5 and 6), but these materials also generally result in poorer processing.

To explore the structure-property relationships between polymer macrostructure and processing, a series of elastomers with well-defined branch structure was synthesized using solution anionic polymerization methods and controlled post-polymerization linking reactions. These poly(butadienes) (PBds) comprise a matrix of two macrostructures at three molecular weights. The macrostructures consisted of linear chains and lout-arm stars that served as a model representing a highly branched system. The macrostructure was determined in solution by multi-angle laser light scattering and solution viscometry. The rheological behavior of the bulk samples was explored by oscillatory shear testing under various conditions. Finally, commercial samples of continuously-produced solution poly(styrene-co-butadiene)rubber (SSBR) were used to validate structure-property relationships in filled compounds. It will be shown that in equivalent formulations, the star-branched products exhibit improved processing at the expense of increased hysteresis.

Background and theory

Anionic polymerization

Solution anionic polymerization is an ideal tool for producing diene-based elastomers with well-defined microstructural and macrostructural features. The living nature of the system assures near quantitative post-polymerization reactions due to negligible termination. In order to optimize a living anionic system to maximize the efficiency of a given post-polymerization linking reaction, several factors must be considered including the nature of the coordinating cation, the polar environment, the monomeric unit at the propagating chain end, and the molar stoichiometry of the linking agent to chain end concentration.

The control afforded by anionic polymerization is attributed to the inherent stability of the anionic propagating center. Of all the alkali metal alkyl initiating systems, the most controlled reactivity is seen when lithium is used as the cation. In conjunction with butadiene monomer, such an organolithium based system produces allylic carbanions that are unique in terms of their structure, reactivity and solvency. Organolithium initiators maintain a partial covalent character to their bonding that allows for aggregation phenomena in hydrocarbon solutions (refs. 7 and 8). The aggregation phenomenon plays an important role in the stability of the propagating center towards side reaction other than propagation (including termination). The advantage of the immediate availability of several reactive centers localized due to aggregation should not be dismissed, and may also provide benefits if post-polymerization linking reactions are used to modify the macrostructure of the chain. As a result, in order to optimize coupling efficiencies, alkyl lithium initiation resulting in an aggregated state of the active chain appears to be preferred.

While lithium PBd maintains the lowest vinyl, highest 1,4 content possible via anionic polymerization (ref. 9), polar modified polymerizations of 1,3-butadiene allow for a wide range of heterotactic vinyl enchainment levels. Polar modifiers comprised of Lewis bases are most often employed to control the level of vinyl structures formed during lithium-based anionic polymerization in non-polar solvents. Relatively small amounts of added polar modifier, based on the stoichiometry to the anionic propagating centers, can have profound vinyl-directing effects (refs. 10 and 11). The use of polar modifiers has deleterious effects on the efficiency of many post-polymerization coupling reactions. The nature of polar modification, especially chelating diamines and diethers (such as N,N,N',N'-tetramethylethylene diamine and ditetrahydrofuryl propane), is to competitively interact with the cation ionically bound to the anionic chain end. This interaction can lead to the dissociation of the chain end aggregate (ref. 12), and a change in the electronic nature and charge density of the allylic species, resulting in increased vinyl enchainment (ref. 13) and a more reactive propagating species. The reactivity of this species toward multifunctional linking agents is tempered by several factors. The presence of a bulky bidentate polar modifier at the chain end may decrease linking efficiencies, similar in effect to the presence of sterically hindered monomer units at the chain terminus (ref. 14).

The structure of a living chain end, therefore, plays an important role in the nature of post-polymerization linking technologies. It has been shown that the linking efficiencies for anionic chain ends are in the order butadienyllithium>isoprenyllithium>styryllithium (refs. 15 and 16). For maximum linking efficiencies, unmodified polymerizations using butadiene monomer in hydrocarbon solvent at relatively low polymerization temperatures is most preferred.

Methods of branching

Commercially, there are several different methods that can be utilized to produce branched structures in anionic polymerization. Most batch-produced anionic polymerization systems exhibit highly linear macrostructures, and the chemistry or process must be changed in order to generate branched structures. Branching can be imparted to the typical anionic polymerization by thermal heating multi-functional monomers, metalation grafting techniques, and post-polymerization linking reactions. Anionic multifunctional initiators can also be used to produce branched (star) macrostructures, but this method has not been used commercially to produce elastomers because of both a limitation on solubility and a lack of molecular weight and polydispersity control due to less-than quantitative initiation reactions.

Heating polydienyllithium chain ends in the absence of monomer can induce coupling due to intermolecular lithium hydride elimination. This reaction can be utilized to impart a degree of branching to a product, albeit in a less-than controlled fashion. Most commercial anionic solution poly(styrene-co-butadiene) polymerizations utilize adiabatic reaction vessels with multiple monomer feed sites to produce random styrene, low vinyl products, although it has been proven that materials with identical microstructures and sequence distributions can be produced at lower temperatures (ref. 17). These adiabatic products also have an elevated degree of branching that is associated with the high temperature polymerization process (refs. 18 and 19).

The addition of bifunctional monomers to a polymerization process is a viable method for producing a variety of branched structures. A common bifunctional monomer that is used for macrostructural modification is divinylbenzene (DVB). When used at low concentrations as a comonomer, DVB produces a long chain branched structure free of gel (ref. 20). DVB is utilized in this manner commercially to branch anionic products whose linearity is a disadvantage due to cold flow issues in storage and handling. DVB can also be used to produce more regular star branched structures by either forming multifunctional initiators (refs. 21 and 22), or by "arm-first" star polymer synthesis using sequential monomer addition of a bifunctional monomer to a preformed branch (refs. 23-25). Due to the random, uncontrolled nature of these techniques, the macrostructure of the resultant products is not as well defined as with more typical multifunctional linking agents.

In commercial anionic polymerization processes involving continuous stirred tank reactors, metalation grafting is not an uncommon side reaction when high vinyl solution products are synthesized (ref. 26). The metalation reaction is promoted by the polar modification used to elevate the vinyl content of some products (refs. 27 and 28). Often, alkali metal alkoxides are also used in conjunction with Lewis base modifiers to achieve even higher vinyl contents (ref. 29). These initiating systems are also superbases, and have been shown to display powerful metalating chemistries (refs. 30-32), especially when used in the presence of elastomer backbones possessing a degree of unsaturation (ref. 33). Grafting techniques are also employed to produce comb-type polymer structures using "grafting-from" technologies (refs. 34 and 35).

In order to produce polymeric materials with well-defined branching structure and to best utilize the living nature of the anionic chain end, it is preferable to use post-polymerization linking reactions to create complex macrostructures. This technique has been used to produce a variety of structures, including simple multi-arm star macromolecules with arms of identical chain length and composition (refs. 10, 36 and 37) and star polymers with arm asymmetry in length and/or composition (refs. 38-41). Star polymers linked about a single atom have been prepared with arm functionalities of 3 and 4 (refs. 42 and 43). By using linking agents with higher degrees of functionality and more complex structure, arm functionalities as high as 6 to 18 have been prepared (refs. 24, 44 and 45). The technique of alternating propagation and linking reactions can be used to synthesize multi-branched dendritic molecules of complex structure (ref. 46).

In most references cited for the synthesis of the different well-defined products above, chlorosilanes of various functionality were used as the linking agents (ref. 47). Four-arm star structures have been used in the past in attempts to elucidate theoretical models of the behavior of branched structures in both dilute solution and bulk rheological studies. In this study, silicon tetrachloride was chosen as the coupling agent to produce the star macrostructure for several reasons. First, the reaction between Si[Cl.sub.4] and butadienyllithium chain ends ([P.sup.-][Li.sup.+]) has been shown to be a quantitative reaction when stoichiometric amounts are used, as in equation.

(1) 4 [P.sup.-][Li.sup.+] + Si[Cl.sub.4] [right arrow [(P).sub.4] Si + 4 LiCl

In fact, it has been shown that by capping the sterically hindered isoprenyllithiun3 or styrewllithitun chain ends with one or more butadiene monomer units, the linking reaction involving Si[Cl.sub.4] can be made to be quantitative (refs. 24 and 48). Second, the only known reaction of allyllithium and silicon halides is that of coupling (ref. 49). However, if alkylchlorosilanes are used as the linking agent, a possible side reaction is that of metal-halogen exchange (ref. 50), resulting in branched species with arm functionalities other than the targeted value, generating a distribution of species with various arm lengths (ref. 51). Finally, highly pure grades of Si[Cl.sub.4] are readily available, and this linking agent is soluble in hydrocarbon solvents.

Rheology

Several review articles and books are available that discuss the molecular theory of polymer viscoelasticity in both the linear and non-linear flow regimes (ref. 52-55). The molecular theories of linear viscoelasticity were initially developed to address dilute solution behavior. Rouse (ref. 56) modeled the viscous and elastic components of a macromolecule by simplifying the structure to a series of segments that behave its Hookian springs where the force constant is based on Brownian motion and is proportional to the temperature of the system. Unfortunately, the Rouse model has no term which accounts for the hydrodynamic interaction phenomenon which describes the interconnectivity of the system and accounts for segment-segment interactions. Zimm (ref. 57) modified the theory and accounted for this interaction. However, the complication of excluded volume (avoiding chain segment interpenetration) was not addressed.

Bueche (ref. 58) has applied the Rouse model for dilute solutions to low molecular weight polymer melts by substituting solvent-polymer interactions with polymer-polymer terms. The Bueche theory implies that at molecular weights below those of entanglement, the zero shear viscosity ([[eta].sub.0]) increases linearly with molar mass. For the case of linear PBd samples el: low molecular weight and narrow polydispersity, this prediction has been verified (refs. 59-61). The linear relationship between viscosity molar mass holds below a characteristic molecular weight ([M.sub.c]), above which the slope increases such that the viscosity can be better fitted by a proportionality of the 3.4 power of the molecular weight (ref. 62).

The modified Rouse theory for unentangled melts also predicts that the longest relaxation time (approximately equivalent to the time required to attain steady flow under constant stress) is proportional to the square of the molar mass. Also predicted is that the steady state compliance ([J.sub.s.sup.0]) increases linearly with molar mass up to a second characteristic molecular weight [M'.sub.c], above which the compliance is independent of molar mass. The calculated values of [M.sub.c] and [M'.sub.c] for lithium poly(butadiene) is 5,900 g/mol and 13,800 g/mol, respectively (ref. 52).

The characteristic molecular weights are evidence that above a certain molar mass, a very different mechanism of chain interaction is manifested. This interaction has been ascribed to entanglements which have been modeled as topological effects defined by the inability of one chain to pass through another. The characteristic molecular weights are evidence of entanglement coupling effects. Here, the restriction on flow must be explained by more than simple hydrodynamic drag or chain-chain friction.

Early on, a theory was developed by Bueche, et al. (ref. 63) to also explain the motion of polymers in concentrated solutions: these concepts were later developed for undiluted polymer melts and introduced two types of motion available to long chains in the melt--free motion of a chain along its own contour and motions perpendicular to the backbone (ref. 64). Unlike the Rouse segmental model, which allows for motion of the bead elements perpendicular to the spring axis, long chains in the melt state cannot move in this manner since they are surrounded by other chains. In any discussion concerning the motion of polymer molecules in the melt, one must first consider the reptation theory of DeGennes (ref. 65). According to the theory, the long chain is relegated to movement along its own contour within the theoretical construct of a tube defined by segments of other chain molecules. The net translation of the polymer chain is accomplished when it has diffused far enough that a new tube hits been established. The time it takes to generate this new tube is equivalent to the configurational relaxation time. Doi and Edwards (ref. 66) have also developed a theory based on the tube construct. They separate molecular motions of the tube to rapid configurational motions between the points of entanglement, and the longer diffusion time required to translate the entire chain relative to the points of restriction. The relaxation times associated with diffusion are much longer than those associated with segmental relaxation. Depending on the polydispersity of the sample, the diffusion of the restriction points may or may not be on the same order its the tube renewal time. Therefore, polydisperse samples may exhibit a distribution of relaxation times compared to the single relaxation time characteristic of a monodisperse system (ref. 67). Edwards and Grant (ref. 68) have suggested that the motion of both the chain and the tube itself should be taken together as cooperative diffusion.

The reptating motion of a chain through points of restriction is central to the theories outlined above. For polymeric materials, shear testing is often used to characterize the viscoelastic response. In systems with linear macrostructure and molecular weights above [M.sub.c] or [M'.sub.c], these mechanical responses of the chain to stress and strain can be explored in the linear viscoelastic regime under small deformations that are applied relatively slowly.

The most common measurements used by academia and industry to probe the linear viscoelastic properties of polymer systems ale taken under oscillatory conditions. Rotational oscillatory viscometers am often used. Both controlled stress (CS) and controlled strain rate (CR) devices are available.

For small strains, the ratio of stress to strain for it viscoelastic solid is a function of time and is defined by the stress relaxation modulus (G(t)). Commonly, a controlled dynamic strain test is performed, in which the sample material is strained sinusoidally, and both the in-phase and out-of-phase components of stress are measured as a function of frequency. G' is the storage modulus which is a measure of the stored (and recoverable) elastic energy in a cyclic deformation, while the loss modulus (G") is a measure of the energy lost as heat. The ratio of G" to G' is defined as the loss tangent, tangent [delta].

The dynamic storage and loss moduli are merely the Fourier sine and cosine transforms of the stress relaxation modulus, which when plotted as a function of time, provide information concerning the viscoelastic behavior and molecular motions of the system. At very short relaxation times that correspond to high frequencies, the material response is glassy in nature and produces a high modulus. As the chain segments relax further, G(t) decreases nearly monotonically with time for low molecular weight chains that do not entangle. But for entangled systems, G(t) falls through a transition period to a zone marked by a relatively flat temporal response where the modulus value remains fixed. This behavior delineates the plateau zone where the modulus response resembles that of a cross-linked network. The time duration of this plateau zone is dependent on the chain length, but the plateau modulus ([G.sub.N.sup.0]) is independent of molecular weight. The apparent length of the segments of polymer chain restricted by the entanglement points can be calculated from the plateau modulus. Equation 2 gives the formula for calculating the entanglement molecular weight ([M.sub.e]) for a linear elastomer above its glass transition temperature from plateau modulus and density ([rho]) data.

(2) [G.sub.N.sup.0] = RT([rho]/[M.sub.e])

The value for [M.sub.e] for lithium poly(butadiene) has been calculated to be 1,900 g/mol (ref. 69). Finally, at very long relaxation times that correspond to low frequencies, the modulus of the entangled system also relaxes in the terminal zone. In this zone, the macrostructure of the polymer chains has the largest effect on the flow behavior as measured by stress relaxation.

Analogous to the stress relaxation modulus curve, a plot of the storage and loss moduli measured as a function of applied frequency under strain amplitudes small enough to maintain a linear viscoelastic response can also provide an illustration of the zones of viscoelastic behavior described earlier for simple shear measurements (refs. 52 and 70). Figure 1 shows an idealized master curve as a logarithmic plot of G' and G" as a function of frequency. Starting at high frequencies (short relaxation times), the glassy zone is defined by little to no configurational rearrangement of the chain backbone in the period of oscillation. A high storage modulus typical of glassy, brittle solids is seen, with the tangent [delta] value near 0.1. As frequencies decrease, the response of the polymer becomes more elastomeric and leathery. A rapid drop in G' and a crossover with G" defines the transition zone, where tangent [delta] values become greater than one signifying that much of the energy put into the system is being lost as heat due to increased chain-chain friction. Limited motions of chain segments between restrictive entanglement points are allowed.

[FIGURE 1 OMITTED]

As frequency drops further, the polymer sample transitions into the plateau zone. In this zone, G' remains relatively constant, but G" reaches a minimum. Tangent [delta] values are very low, as the elastic component dominates the response. At these frequencies, there is enough time for the chain segments bound by entanglement points to change conformation and store energy through an entropic mechanism. However, there is not enough time allowed for molecular translation by diffusion. G' in this region corresponds to the plateau region of the G(t) curve that is used to determine [G.sub.N.sup.0].

As the frequency of measurement becomes even lower, the terminal zone is reached. In this zone, the chain mobility is characterized by free flow and molecular translation. Again, G' crosses G" and tangent [delta] values increase above 1.0. The effect that various macrostructural features have on chain mobility is most easily seen in this zone. The plateau zone is very well defined for monodisperse polymers. However, as the polydispersity increases, the transition between the plateau zone and the terminal zone becomes less distinguishable. The transition into the terminal zone is also shifted to lower frequencies with an increase in the molecular weight of mono-disperse systems.

The prior discussions assumed that the measurements were taken while the system was in the linear viscoelastic regime. However, in the case of larger deformations or rates of deformation, the system may exhibit non-linear rheological behavior. With large strains and rates of deformation, there are large displacements of the polymer chains from the random coil configurations central to the molecular theories that describe linear viscoelastic behavior. Theories based both on empirical equations and molecular theory have been offered to model the complex response of entangled polymers under such non-linear conditions. These theories have been well summarized in several books and articles (refs. 53, 54 and 71), however, no universal set of equations describing non-linear flow has been established.

Graessley's molecular theory for the shear-rate dependence of viscosity has been successful in explaining the select experimental data (ref. 72). At high shear rates, the time allowed for the formation and dissolution of entanglements is very short since the interaction time for two molecules whose random coil dimensions are overlapped is brief. Therefore, the apparent concentration of entanglements is decreased as shear rates are increased, and since the time required to form an entanglement is proportional to the viscosity at a given shear rate, the apparent viscosity is also lowered.

The viscosity of a polymer melt approaches the constant value [[eta].sub.0] only at low shear rates. As the shear rate is increased, there is typically a negative departure from [[eta].sub.0]. At high shear rates, most polymers exhibit a rate-dependent decrease in the viscosity that is typically manifested by a power-law dependence on shear rate. The actual shear rate where viscosity departs from [[eta].sub.0] is dependent on the macrostructure of the sample and is referred to as the characteristic shear rate ([[gamma].sub.0]). For linear polymers with low polydispersities, the characteristic shear rate increases as the molecular weight increases (refs. 73 and 74). However, an increase in the polydispersity of the sample lowers the characteristic shear rate and also makes the transition into the non-linear regime both less distinct (ref. 1) and move to lower characteristic shear rates (ref. 72). For linear polymers, the reciprocal of the characteristic shear rate is the characteristic relaxation time which correlates to the time required for complete configurational rearrangement of an entangled polymer molecule. However, with branched polymers configurational rearrangement of the backbone, as well as the chain appendages, prohibit such a simplistic assignment as a characteristic relaxation time (refs. 1 and 75).

Commercial relevance

Using linking agents to modify the macrostructure of commercially produced elastomers is a common practice. Many tire elastomers produced for high performance applications are coupled with various linking agents to alter their processing characteristics and the performance of the resulting tire tread product. Silicon tetrachloride (refs. 76 and 77) and tin tetrachloride (refs. 43 and 78) are common tetrafunctional linking agents used in synthetic rubber produced for the tire industry.

Complex changes in macrostructure will impact the processing characteristics of the elastomer. Important processing properties such as cold flow, behavior on a mill or calendar, mixing characteristics, shrinkage, die swell and quality of the extrudate are all determined by macrostructure. The addition of long chain branching has been shown to alter these processing properties. A comprehensive review has been published outlining the relationships between raw elastomer structure and the effect seen when materials of different branching content are processed through commercial equipment (ref. 79). Long chain branching will lengthen the relaxation times of a polymer due to increased entanglements. Increasing the branching content can also result in improved mill shrinkage, green strength and die swell, and can alter the milling and mixing behavior by increasing the elastic memory of the elastomer.

Tests that most accurately predict processing performance would have to determine the rheological behavior of a material at various shear rates. The downfall of using Mooney viscosity as a processing indicator is that the value generated from this test is a single rheological measurement that cannot accurately represent the behavior of a sample over various shear rates and kinematics of deformation (ref. 80). The bulk viscosity of an elastomer is dependent on a variety of macro-structural features. It is possible to produce elastomers with the same Mooney index, but varied macrostructures such that their performance under processing conditions would be disparate (ref. 81).

It has been suggested that in order to best predict the performance of an elastomer under high shear processing conditions (i.e., internal mixing and extrusion), testing at low shear rates is required to accentuate the differences in the polymer rheology (ref. 82). At high shear rates, the processing characteristics are dominated by the elastic component of viscoelasticity, and this behavior can be controlled by small amounts of material in a sample that possess either very high molecular weights or high degrees of branching. To best detect these minute differences, flow curves generated at low shear rates are perhaps the best measurements.

This first part of this study examined the ramifications of introducing long chain branching on the linear and non-linear viscoelastic behavior of PBd samples of well-defined macrostructure. Model four-arm star samples, produced via linking reactions using silicon tetrachloride, were compared to their linear counterparts of equivalent molecular weight. The relationship between polymer structure, theological measurements, and compound processing and hysteresis will be further explored in the second part of the study using commercially available linear and coupled SSBR products.

References

(1.) F.C. Weissert and B.L. Johnson, Rubber Chem. Tech., 40, 590 (1967).

(2.) M.L. Kerns, S.K. Henning and M.J. Rachita, in Butadiene Polymers, Encyclopedia of Polymer Science and Technology, John Wiley & Sons, Inc., 2002.

(3.) H. Colvin and S. Henning, Tire Tech. Intl., Ann. Rev., 32 (2001).

(4.) J.E. Mark, B. Erman and F.R. Eirich, eds., Science and Technology of Rubber, Academic Press, New York, 1994.

(5.) P.J. Flory, Principals of Polymer Chemistry, Cornell University Press, Ithaca, 1953.

(6.) S.L. Aggarwal, H.J. Fabris, I.G. Hargis and R.A. Livigni, Polym. Prepr.-Am. Chem. Soc. Div. Polym. Chem., 26, 3 (1985).

(7.) C. Lambert and P. von R. Schleyer, Angew. Chem. Int. Ed. Engl., 33, 1,129 (1994).

(8.) B. Wakefield, The Chemistry of Organolithium Compounds, Pergamon Press, Oxford, 1974.

(9.) F.C. Foster and J.L. Binder, Advances in Chemistry Series No. 19, Am. Chem. Soc., 1957.

(10.) H.L. Hsieh and R.P. Quirk, Anionic Polymerization: Principals and Practical Applications, Marcel Dekker, Inc., New York, 1996.

(11.) T.A. Antkowiak, A.E. Oberster, A.F. Halasa and D.P. Tate, J. Appl. Polymer Sci., 10, 1,319 (1972).

(12.) R. Milner, R. Young and A.R. Luxton, Polymer, 24, 543 (1983).

(13.) S. Bywater, in Recent Advances in Anionic Polymerization, T. Hogen-Esch and J. Staid, eds., Elsevier, New York, 1987.

(14.) J.C. Cho, K.H. Kim, K.U. Kim, S. Kwak, J. Kim, W.H. Jo, M.S. Chun, C.H. Lee, J.K. Yeo and R.P. Quirk, J. Polym. Sci., 36, 1,743 (1988).

(15.) B.J. Bauer and L.J. Fetters, Rubber Chem. Tech., 51, 406 (1978).

(16.) V. Ruiz Santa Quiteria, C.A. Sierra, J.G. Fatou, C. Galan, and L. Fraga, paper #78 presented at the 148th ACS Rubber Division Meeting, 1995.

(17.) M.L. Kerns, Z. Xu and S. Christian. paper #158 present ed at the 156th ACS Rubber Division Meeting, 1999.

(18.) N. Sommer, Kautsch. Gummi, 28, 131 (1975).

(19.) JP 47-2688 assigned to Asahi Chemical Industry.

(20.) H. Eschwey and W. Burchard. J. Polym. Sci., Polym. Symp., 53, 2 (1975).

(21.) W. Burchard and H. Eschwey, Polymer; 16, 180 (1975).

(22.) P. Lutz and P. Rempp, Makromol. Chem., 189, Ik,051 (1988).

(23.) C. Strazielle and J. Herz, Europ. Polym. J., 13, 223 (1977).

(24.) M. Hadjichristidis, A. Guyot and L.J. Fetters, Macromolecules, 11, 889 (1978).

(25.) D.H. Rein, P. Rempp and P.J. Lutz, Macromol. Chem. Phys., 199, 569 (1998).

(26.) M.L. Kerns and S.K. Henning, Rubber Chem. and Tech., 75, 299 (2001).

(27.) D.P. Tate, A.F. Halasa, F.J. Webb, R.W. Koch and A.E. Oberster, J. Polym. Sci., 9, 139 (1971).

(28.) M. Farral and J. Frechet, J. Org. Chem., 41, 3,877 (1976).

(29.) H.L. Hseih and C.F. Wofford, J. Polym. Sci., 7, 449 (1969).

(30.) T. Kremer; S. Harder; M. Junge and P. Schleyer, Organometallics, 585 (1996).

(31.) M. Sclosser, Pure & Appl. Chem., 60, 1,627 (1988).

(32.) L. Lochmann, Eur. J. Inorg. Chem., 1,115, (2000).

(33.) A.F. Halasa, G.B. Mitchell, M. Stayer, D.P. Tate, A.E. Oberster and R. W. Koch, J. Polym. Sci., 14, 497 (1976).

(34.) H.A.J. Battaerd and G.W. Tregear; Graft Copolymers, Interscience, New York, 1967.

(35.) R.J. Ceresa, ed., Block and Graft Copolymerizations, Vol. 1 and 2, Wiley-Interscience, New York, 1973.

(36.) K. Hatada, T. Kitayama and O. Vogl, Macromolecular Design of Polymetric Materials, Marcel Dekker, New York, 1997.

(37.) P. Rempp, E. Franta and J.-E. Herz, Adv. Polym. Sci., 86, 145 (1988).

(38.) R.W. Pennisi and L.J. Fetters, Macromolecules, 21, 1,094 (1988).

(39.) R.P. Quirk and T. Roo, Polym. Bull., 29 (1993).

(40.) Y. Tselikas, N. Hadjichristidis, R.L. Lescanec, C.C. Honeker, M. Wohlgemuth and E.L. Thomas, Macromolecules, 29, 3,390 (1996).

(41.) H. Iatru, E. Siakali-Kioulafa, N. Hadjichristidis, J. Roovers and J.W. Mays, J. Polym. Sci., Polym. Phys., 33, 1,925 (1995).

(42.) R.P. Zelinski and C.F. Wofford, J. Polym. Sci., 3, 93 (1965).

(43.) C.A. Uraneck and J.N. Short, J. Appl. Polym. Sci., 14, 1,421 (1970).

(44.) J.E.L. Roovers and S. Bywater; Macromolecules, 5, 385 (1972).

(45.) N. Hadjichristidis and L.J. Fetters, Macromolecules, 13, 191 (1980).

(46.) F. Wang, J. Roovers and PM. Toporowski, Macromol. Symp., 95, 205 (1995).

(47.) M. Morton, T.E. Helminiak, S.D. Gadkery and F. Bueche, J. Polym. Sci., 57, 471 (1962).

(48.) L.J. Fetters and M. Morton. Macromolecules, 7, 552 (1974).

(49.) D. Wittenburg and H. Gilman, Quart. Rev., 13, 116 (1959).

(50.) R.G. Jones and H. Gilman, Org. Reactions, 6, 339 (1951).

(51.) T. Altares, Jr., D.P. Wyman, V.R. Allen and K. Meyersen, J. Polym. Sci., A, 3, 4,131 (1965).

(52.) J.D. Ferry, Viscoelastic Properties of Polymers, 2nd Ed., Wiley; New York, 1970.

(53.) J.M. Dealy and K.F. Wissburn, Melt Rheology and its Role in Plastics Processing, Van Nostrand Rheinhold, New York, 1990.

(54.) W.W. Graessley, Adv. Polym. Sci., 16, 1 (1974).

(55.) G. Kraus, in The Stereo Rubbers, W.M. Saltman, ed., Wiley, New York, 1977.

(56.) P.E. Rouse, Jr., J. Chem. Phys., 21, 1,272 (1953).

(57.) B.H. Zimm, J. Chem. Phys., 24, 269 (1956).

(58.) F. Bueche, J. Chem. Phys., 20, 1,959 (1952).

(59.) J.T. Gruver and G. Krause, J. Polym. Sci., 2, 797(1964).

(60.) H.H. Meyer and W. Ring, Kaut. Gummi Kunstst., 24, 526 (1971).

(61.) G. Kraus and J.T Gruver, J. Polym. Sci., 3, 105 (1965).

(62.) G. Berry and T. Fox, Adv. Polym. Sci., 5, 261 (1968).

(63.) F. Bueche, W.M. Cashin and P. Debye, J. Chem. Phys., 20, 1,956 (1952).

(64.) F. Bueche, J. Chem. Phys., 25, 599 (1956).

(65.) P.G. DeGennes, J. Chem. Phys., 55, 572 (1971).

(66.) M. Doi and S.F. Edwards, The Theory of Polymer Dynamics, Oxford University Press, 0xford, 1986.

(67.) M. Doi, W.W. Graessley, E. Helfand and D.S. Pearson, Macromolecules, 20, 1,900 (1987).

(68.) S.F. Edwards and J.W.V. Grant, J. Phys. A: Math. Nucl. Gen., 6, 1,169 (1973).

(69.) R.G. Mancke, R.A. Dickie and J. D. Ferry, J. Polym. Sci., 6, 1,783 (1968).

(70.) I.M. Ward, Mechanical Properties of Solid Polymers, Wiley, New York, 1971.

(71.) D.S. Pearson, Rubber Chem. Tech., 60, 439 (1987).

(72.) W.W. Graessley, J. Chem. Phys., 47, 1,942 (1967).

(73.) R.A. Stratton, J. Colloid Sci., 22, 517 (1966).

(74.) E. V. Menezes and W. W. Graessley, J. Polym. Sci: Polym. Phys., 20, 1,817 (1982).

(75.) A. Ghijels and H.J.M.A. Mieras, J. Polym. Sci: Polym. Phys., 11, 1,849 (1973).

(76.) W.L. Hsu, et al., US 5,422,403 (1995).

(77.) D.J. Zanzig, et al., US 5, 798,448 (1998).

(78.) F. Tsutumi, M. Sakakibara and N. Oshima, Rubber Chem. Tech., 63, 8 (1990).

(79.) J.L. White, Rubber Chem. Tech., 42, 257 (1969).

(80.) N. Nakajima, Polymer International, 36, 105 (1995).

(81.) B.M.E. Van der Hoff, Rubber Plast. Age, 46, 821 (1965).

(82.) N. Nakajima, Journal of Elastomers and Plastics, 32, 46 (2000).