Chapter 23
Liquid-Crystalline Polymers A Unifying Thermodynamics-Based Scheme 1
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A. Keller , G. Ungar , and V. Percec Downloaded by UNIV OF MINNESOTA on October 14, 2014 | http://pubs.acs.org Publication Date: August 24, 1990 | doi: 10.1021/bk-1990-0435.ch023
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H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom Department of Macromolecular Science, Case Western Reserve University, Cleveland, OH 44106
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It i s shown that conditions for realizing mesomorphic states i n polymers are readily expressed i n terms of the relative thermodynamic s t a b i l i t i e s of the crystal line, liquid crystalline and liquid phases. The simple scheme here presented has the merit of providing: i ) a unifying perspective over a wide range of mesophase behavior which otherwise may be considered in isolation as disconnected occurrences, ii) a signpost for pur poseful attainment (or enhancement) of the mesomorphic state also i n the case of systems which are not normally considered liquid crystal forming, andiii)an explanation for the dependence of the mesomorphic temperature range as a function of the degree of poly merization. Examples are quoted from a range of mate r i a l s most comprehensively from polyethylene, bringing together diverse past and some rather striking new ob servations illustrating the validity and usefulness of the scheme. In recent years the mesomorphic state has come increasingly to the forefront of polymer science, p a r t i c u l a r l y since the purposeful synthesis and study of polymeric l i q u i d c r y s t a l s . Most frequently i t i s associated with the presence of mesogenic groups, (such as on t h e i r own would form small molecular l i q u i d c r y s t a l s ) b u i l t i n , or attached to, the macromolecular chain where the mesomorphic state is usually a t t r i b u t e d to the s t i f f n e s s imparted by these groups. In other instances of mesophase forming s t i f f molecules the chains are too i r r e g u l a r to c r y s t a l l i z e i n which case the suppression of c r y s t a l l i z a t i o n i s considered as the factor which promotes the mesophase. However, there are chains, including quite regular ones, which can give r i s e to the l i q u i d c r y s t a l l i n e state without 3
Current address: Division of Ceramics, Glasses, and Polymers, University of Sheffield, Sheffield S10 2TZ, United Kingdom 0O97-6156/90/0435-O3O8$O7.75/0 © 1990 American Chemical Society In Liquid-Crystalline Polymers; Weiss, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990.
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23. KELLER ETAL.
A Unifying Thermodynamics-Based Scheme
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any constituent capable of forming l i q u i d c r y s t a l s as separate small molecules. Such are e.g. the polymers based on the f l e x i b l y jointed diphenyl compound diphenyl ethane (1), the t o t a l l y f l e x i b l e main chain polysiloxanes with side groups beyond the length of me thyl (2), main chain polyphosphazenes (3) and even the f u l l y f l e x i b l e and chemically simplest long chain compound polyethylene under circumstances to be discussed i n s p e c i f i c d e t a i l below. Many examples of mesophases i n polymers of the l a t t e r type have been l i s t e d i n the review by Wunderlich et a l . (4). The purpose of the present p u b l i c a t i o n i s to lay out a simple thermodynamic scheme which embraces a l l the above categories. I t w i l l be purely diagrammatic and q u a l i t a t i v e , along f a m i l i a r l i n e s , yet we hope that i n the context presented i t w i l l provide a coherent thread l i n k i n g t o gether the various manifestations of mesophases, thus contributing towards the understanding of their i n t e r r e l a t i o n s h i p and providing guidance for t h e i r purposeful design. I l l u s t r a t i v e examples w i l l be quoted from a v a i l a b l e experimental material such as are not r e a d i l y found a l l together i n the l i t e r a t u r e at l e a s t i n the present context. Such w i l l embrace cases with chemical c o n s t i t u t i o n and/or physical parameters as v a r i a b l e s . They w i l l include some examples of chains with varying r a t i o s of r i g i d and f l e x i b l e constituents but mostly polyethylene i n i t s diverse forms and circumstances. F i n a l l y , the dependence of phase t r a n s i t i o n temperatures on molecul a r weight w i l l be discussed based on the same p r i n c i p l e s . Equilibrium States For the considerations to follow i t w i l l s u f f i c e to consider the basic thermodynamic r e l a t i o n s h i p dG = Vdp - SdT
(1)
where G i s the free energy, S the entropy, V the volume, p the pressure and T the temperature. For the scheme i n question take f i r s t the melting of a true c r y s t a l at constant pressure (dp=o). As seen from Figure l a , and as follows from Equation 1, the free energies of both c r y s t a l (G.) and i s o t r o p i c l i q u i d (G.) decrease with increasing temperature where the decrease i n G^ i s the steeper, due to S ^ S j ^ Where G^ crosses G, the c r y s t a l melts, which of course i s at T^_. = T , the melting point of the c r y s t a l . In t h i s case, as drawn In Figure l a , the free energy of any hypothetical mesophase ( i f such can e x i s t at a l l ) , G^ , cannot f a l l below both G, and G^, hence correspond to a stable s*tate at any temperature, while decreases f a s t e r with T than G, i t w i l l only cross at G^ at a poin£ which i s above G., i . e . where the i s o t r o p i c l i q u i d i s already the s t a b l e s t phase. Tnus the mesophase i s v i r t u a l and remains u n r e a l i z able as a stable phase. In order to create a stable mesophase a section of the G^ versus T curve w i l l need to be brought beneath both G^ and G. (thus to a state of greatest s t a b i l i t y ) . This can be achieved either a) by r a i s i n g G^ (Figure l b ) , or b) by r a i s i n g G, (Figure l c ) , or by a combination of both a) and b). As seen i n figures lb and l c the mesophase w i l l be "uncovered" i n a temperature range bounded by k-1 * lc-i i P di g temperatures of c r y s t a l melting and S-sotropization respectively. (The lowering of G.. would have c
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In Liquid-Crystalline Polymers; Weiss, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990.
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Tl=T|c-l T =Tk-lc
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Figure l a . Schematic p l o t of free energies v s . temperature for a scheme that does not show a mesophase. G, , and are, r e s p e c t i v e l y , the free energies of the c r y s t a l l i n e , mesomorphic ( v i r t u a l ) and i s o t r o p i c l i q u i d s t a t e s . T j . = T i s the c r y s t a l l i n e melting point. Here, as i n subsequent Figures lb and l c , the heaviest l i n e s correspond to the s t a b l e s t state at a given temperature. m
T =Tk-lc
T|=T|c-l
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Figure l b . Schematic p l o t of free energies v s . temperature for the system i n Figure 1 but with G raised (to G ^ ) so as to "un cover" the mesophase. k_i *i -i y ^-~ °^ t r a n s i t i o n and the i s o t r o p i z a t i o n t r a n s i t i o n temperatures. T
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In Liquid-Crystalline Polymers; Weiss, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990.
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23. KELLER ETAL.
A Unifying ThermodynamicS'Based Scheme
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Figure l c . Schematic p l o t of free energies vs. temperature for the system i n Figure l a but with G raised (to G^ ) so as to "uncover" the mesophase. 1
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In Liquid-Crystalline Polymers; Weiss, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990.
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LIQUID-CRYSTALLINE POLYMERS
the same effect; but changes i n G are expected to be small com pared to those i n G and G ancf w i l l be disregarded i n what follows.) In general, r a i s i n g of G. (case a) arises from the lowering of the melt entropy, while r a i s i n g of G, (case b) from the reduction i n the perfection of the c r y s t a l as to be shown i n spe c i f i c examples l a t e r . Note that i n case of a) the c r y s t a l melting point, T , i s r a i s e d , while i n b) i t i s lowered, a s i t u a t i o n c l e a r l y brought out by the experimental examples to be quoted, combination of both a) and b ) . As seen i n Figures lb and l c the mesophase w i l l be "uncovered" i n a temperature range bounded by T^_ and T-_=T^ corresponding to temperatures of c r y s t a l melting and i s o t r o p i z a t i o n r e s p e c t i v e l y . (The lowering of G.. would have the same effect; but changes i n are expected to De small com pared to those i n G. and G^ an£ w i l l be disregarded i n what follows.) In general, r a i s i n g of G^ (case a) arises from the lowering of the melt entropy, while r a i s i n g of G. (case b) from the reduction i n the perfection of the c r y s t a l as to be shown i n spe c i f i c examples l a t e r . Note that i n case of a) the c r y s t a l melting point, T , i s r a i s e d , while i n b) i t i s lowered, a s i t u a t i o n c l e a r l y brought out by the experimental examples to be quoted. We can generalize further by considering the influence of change i n pressure, i . e . the Vdp term i n Equation 1. Usually the s p e c i f i c volume i s larger for the l i q u i d than for the c r y s t a l with the mesophase expected to l i e i n between; hence (SG^/Sp) «>(
