Chain Conformational Statistics and Mechanical Properties of

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Chapter 19

Chain Conformational Statistics and Mechanical Properties of Elastomer Blends 1

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2

Milenko Plavsic , Ivana Pajic-Lijakovic , and Paula Putanov 1

Faculty of Technology and Metallurgy, Belgrade, Serbia and Montenegro Serbian Academy of Sciences and Arts, Belgrade, Serbia and Montenegro

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Design of mechanical properties, especially the relation between tensile and dynamic moduli in terms of chain conformational statistics isconsidered.Data on new elastomer blends with gradient properties, able for mixing on molecular level and partial networking with separation of phases, are analyzed in parallel to classical commodity materials. Especial attention is paid to synergetic effects oftheincrease of blend modulus, relative to moduli obtained by linear "rule of mixtures" for component polymer moduli, described by Kleiner-Karasz-MacKnight equation, and new models based on self-similar scaling of elastomer network dynamics. New data on model blends exposing synergetic effects with the change of conformational statistics are presented as well.

252 In New Polymeric Materials; Korugic-Karasz, L., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2005.

253


Polymer blends achieved among commodity materials in last forty years importance, which alloys realized for many centuries of metal production experience. One of most attractive opportunities that blends afford is obtaining desirable properties that may not be available in the component homopolymers, in quantitative or qualitative sense. For example, an increase of elastic modulus of some plastics as well as elastomer blends, over the modulus of each component, formulated quantitatively by Kleiner- Karasz- Mac Knight equation, is often of high practical importance (1-3):

E = φ Ε -f φ Ε + φ φ β b

χ

χ

2

2

χ

2

(1)

ί2

where Ει, E , φι and φ represent the moduli and composition of components respectively and β η represents relation between 50/50 blend and components moduli. Fundamentally, it indicates some synergetic interactions between component polymers. It is derived considering tensile properties of a series of blends of truly miscible components: polystyrene (PS) and poly(2,6-dimethyl1,4-phenylene oxide) (ΡΡΟ), which provide the basis also for the family of engineering thermoplastics called Noryl®. Similar increase of tensile moduli exhibits a number of blends of noncompatible elastomers , without and with filler, e.g. chlorobutyl rubber (CIIR) with natural rubber (NR), silicone rubber (MQ) with NR, styrene-butadiene rubber (SBR) and styrene-acrylonitiyle (NBR) (3-6). At die first glance, such synergetic improvement of mechanical properties seems to be effect of quite a general type for polymer blends. But, more detailed analyses face at once a number of difficulties. The change of plateau moduli G ° with blend composition of PS/PPO estimated from dynamic measurements of Porter and Lomellini (7,8), exhibit just the opposite effect: lower values of blend moduli then the simple linear "rule of mixtures", described by equation: G ° =(PiG ° + ipfim' predicts (see also Figure 1). Kleiner at al. correlated in elegant way eq 1 with a simple structural parametar as blend density gradient (1). A couple of years later Gressley and Edwards correlated G ° in general, with number of chains per unit volume and chain length, considering entanglement effects (9). Recently, Edwards and Terentjev published rigorous analyses of real entangled networks at low-frequency regimes, but as Terentjev pointed, there is still much to be understood about mechanism of dynamic response of elastomer networks (10,11). On the other hand, a number of mechanical properties of elastomer blends can be correlated easily with conformational features of component molecules for behavior predicting and design of high performance compounds. Moreover, these relations, in some cases, could be further correlated to self-similar scaling of network properties. In this contribution we try both, to review "the state of art" in fully cured network moduli scaling, and to correlate moduli with chain conformational statistics. We look in particular for explanation of and possibilities for synergetic effect in some new elastomer blends, and design of materials in general. 2

2

N

m

N1

N

In New Polymeric Materials; Korugic-Karasz, L., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2005.

254

Theoretical Background The basic knowledge providing research background for the issues of interest here, are polymer networking theories and rubber elasticity theories, connected with chain conformational statistics. The one, who gave fundamental contribution to the all threefields,with his theories, ideas and intuition was P. J. Flory. Thefirsttheory of polymer networking is formulated by Flory in 1941 (12). It provides formula for probability p of a network arising in polymer systems: p = [ 1 / ( fil) ]~ ( 1 / Ν ). It startsfromreaction probabilities of functional groups of molecules building die network, which are simply proportional to theirfractionsin the reaction mixture, and takes into account neither die space architecture nor the steric hindrances in the course of network developing. Still, it has been very successful in prediction behavior of many systems, in particular vulcanization of rubbers. (In previous equation / is functionality of growing structures and Ν degree of polymerization). That encouraged development of new theories, to include network architecture, as e.g. cascade theory of Gordon and others (13). It connecte networking kinetics with space organization, describing process by cascade of network branches, extending all over the system, what immediately makes connection to graph theory in mathematics. But, we knowfromvulcanization chemistry, that grow of network starts from accelerator-activator complex nuclei, spread all over the system. It extends in space and time, till percolation threshold i.e. an especial type of bond connectivity. It can be described as appearance of indefinitely polydisperse ensemble of randomly branched polymers at the gel point (GP). Further reaction progress makes the network denser. Such clustered structure can be described in elegant way, in terms of fractal geometry developed by Mandelbrot, byfractaldimension d (14). Both analogues, graphs and fractals, provide a background for generalization, bat have hidden danger of misinterpretation of network connectivity. For example, conformation of a polymer chain can be also described byfractaldimension. But, it should be considered as an effect resultingfromtopology of bond connections, short and long range interactions of the chain and environment influence as well, and not a geometrical feature. It is in fact multi -body interaction effect, what is very tough problem in physics. Flory was diefirstwho succeeded to avoid some difficulties for polymer systems and offer solution with his excluded volume theory (12% what can be expressed also by power low:


c

c

f

N = ARg

(2)

where R is characteristic length (radius of gyration) and Ν degree of polymerization of the chain. Exponent describing non-asymptotic scaling of a G



255 polymer chain with increase of the length due to excluded volume effect, is D=5/3. If the effect is screened, D=2 ("Flory's theorem") In terms of the theory of scaling of physical properties with structure relations, developed by P. J. de Geenes (75), exponent D is a global feature of general validity for polymer molecules (or generally speaking, for some class of systems) describing some essential features of chain structure, while prefactor A represents local properties characteristic for each polymer type. But, as we know, scaling exponents determined experimentally for some new scaling relations, vary significantly. It indicates interfering of some other phenomena that should be extracted from scaling relation, or a need of redefinition of class of systems, it is valid for. Considering cluster connectivity, (what is of especial interest for our problem), should be pointed to spectral dimension d defined first by Alexander and Orbach (16) It could be extracted from scaling relations for clusters of different topology e.g. different types of networks. By definition, scaling of N (the number of distinct sites on the lattice visited by random walk) with U (number of steps, or time) is described by d/2 The average radius of walk can be easily connected to radius of gyration R in eq 2. Returning to die network connectivity described by cascade theory, it should be pointed that, according to percolation theory developed by Stauffer and de Gennes,(77) scaling of cluster distribution in die vicinity of GP is false. Reason is simply, the false representation of connectivity of the cascade, not taking into account steric hindrances. S9

t

G

Modulus and Connectivity Levels De Germes is the first who recognized connectivity relationship in modulus scaling ("electrical analogy" (75)). On the other hand, connectivity is extensively discussed issue in rubber elasticity theories. In the first theory, based on contributions of Kuhn, Wall and Flory (3,72), proposed Flory incorporation in kT/Mc prefactor correction (1 - 2Mc/M) (Mis initial molecular weight), because dangling chains do not transfer stress. Later, extensive literature has been accumulated on semi- phenomenological model of entanglement connectivity, including theories of entanglement effects in blends as well (5). But, opposite to entanglement view, Flory in the mean field approach of constraint on junctions theory, incorporated cycle rank of the cluster as connectivity measure: Ψ =^+7n . Here n and n are numbers of vertices and chains in a spanning tree. For a perfect phantom network (having no dangling chains and large n ), Ψ =n - n and n = (f /2)N ,(where / is crosslink functionality). Thus, the prefactor in James and Gouth type modulus is just the cycle rang: n (l-2 / f) kT/2, while for affine network; Ε = ripkT / 2. Using "electrical analogy" can be shown (3) that the mean - to -end network segment separation , affine deformed, but with c

c

p

c

p

C

p

2


p

c


256 die contribution of afluctuationterm independent of deformation, gives die same moduli relation. Dependence on 2 / f for phantom network turns up in the application of path integral method, as well. So, essential difference of real network (being with modulus between phantom and affine model) is additional degree of constrains onfluctuations,in the mean field approach. In can be understood simply, as decrease of connectivity with extension in dense system of high sequential mobility, ( as can be seenfromtheories of Flory, Erman and Mark (18)). Viscoelasticity aspect is introduced to percolation theory postulating distribution of relaxation times due to existence offractaldomains, with θ and θ as lower and upper time limit, respectively, Indeed,firstWinter and Chanbon and a number of authors later (19-22), showed that at the gel point, the distribution of relaxation times obeys a power law: 0

ζ

ά

Η(θ)ά]ϊίθοοθ' ά]ϊίθ

(3)

The shear relaxation can be obtain by : 00

G(t) = \[Η{Θ)Ιθ]

tie

ά

e deocΓ

(θ

Chain Conformational Statistics and Mechanical Properties of

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