Hydrogels for Medical and Related Applications

15 The Hydrogel-Water Interface

Downloaded by MIT on June 7, 2013 | http://pubs.acs.org Publication Date: June 1, 1976 | doi: 10.1021/bk-1976-0031.ch015

A. SILBERBERG The Weizmann Institute of Science, Rehovot, Israel

There are very few investigations which deal with the gel-swellingmedium interface specifically. The distribution of solute components according to size or affinity is considered in treatments of gel chromatography. Contact angle measurements have been undertaken routinely (1), but the structure and the statistical mechanics of this type of interphase has received only a preliminary treatment (2). In selecting the hydrogel-water interface for special consideration, it will have to be realized that it does not possess features which are not characteristic of the gel-solvent interface in general and that the measure of our ignorance is probably about the same. This is provided, of course, that we put aside - as we shall do here - such special potential aspects as charged ionic surface groups and long range electrostatic interactions. Still, even without charge interactions, water is a rather special solvent and the uncharged polymeric species which are soluble, or swellable, are so, generally, because they possess groups which hydrate well, i.e. will form a hydrogen bond with water. Such groups are almost always also capable of forming hydrogen bonds with each other and solubility, in general, implies that the hydrogen bond with water is not too weak as compared with the bond dimerizing two groups. While in water both the solution and dimerization bond energies tend to be quite large, they are also about equal and their difference remains small. Solubility, i.e. sweliability, of the material will be assured if the interaction between the polymer segments in the aqueous environment is only mildly attractive, i.e. does not overfavor dimerization over hydration (see Figure 1). Similar considerations will apply to gels in general. Nevertheless, some special aspects govern aqueous gels which could cause them to behave differently to other gels.

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In Hydrogels for Medical and Related Applications; Andrade, J.; ACS Symposium Series; American Chemical Society: Washington, DC, 1976.


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Energy Level Scheme

[ pp w

(a)

w

oo ~ 2 op] ~ ~ ^ w

(b)

Figure 1. Energy effects which control stability. w , energy level for polymer segment bound to solvent; w , energy level for polymer segment-polymer segment interaction; w , energy level for solvent-solvent interaction. According to the Flory-Huggins theory of polymer solutions, χ = [2w — w — w ]/2kT < 0.5 for solubility. The parameter χ is generally found to be in the range between 0 and 0.5. This implies, as the potential diagram (b) shows, that the "pp"-bond is probably stronger than the "op"-bond. If, how ever, it is too strong, then χ > 0.5, and the system is potentially unstable. Hence, the hydrogen bond between gel substance groups can be somewhat stronger than the hydro gen bond of this group with water but not very much stronger. op

pp

00

op

00

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Features which Distinguish Hydrogels Whereas i n most non-polar solvents the mixing energies are due to van der Waals interactions only (both the individual energy level changes and their differences are small), i n aqueous environments we are dealing with relatively large energy effects. Hence the same percentage change can produce much larger effects on solubility i n the aqueous medium. Conformational changes and cooperative interactions between polymer and polymer and polymer and solvent are thus much more dramatic and much more readily precipitated i n aqueous media than i n other environments. A hydrogel can be regarded as a potentially unstable system whose state i s easily influenced by slight variations i n temperature,or pressure, or by minor chemical modifications of the aqueous environment (e.g. addition of small amounts of such solutes as neutral salts or alcohols). To the extent that gradients exist i n the gel, particularly in the surface region, we might thus be faced with the p o s s i b i l i t y of large changes i n conformation (or degree of interaction between the segments of the gel substance) i n going through the i n t e r f a c i a l region between bulk homogeneous gel and bulk water. The Gel-Solvent Interface Gels are characterized by the possession of crosslinks. Generally speaking these are chemical units to which a number of chains, three or more, are linked i n some fashion either by permanent bonds or by bonds of a sufficiently long lifetime so that changes i n structure do not occur, or occur only very slowly under stress. These crosslinks, however, need not be defineable chemical links between separate chains, but could, for example, be more extensively organized regions containing a larqe amount of gel substance between-, which a small number of long coiling polymeric chains establish the connections and hold the gel together, topologically. These organized regions thus act as effective crosslinks and the chain segments between them as the effective network segments. © are comparing the actual gel with the classical homogeneous ideal, three-dimensional network model and try to establish correlations. These correlations w i l l depend upon the experiment considered and i t i s not to be expected that the division into effective crosslinks and effective network segments need necessarily be unique. The kind of d i v i sion which w i l l account for the elastic modulus may not correspond to the division best suited to permeation studies. The main points to remember are that gel structure i s not necessarily homogeneous,that not each chemical crosslink i s an effective crosslink,but that a meaningful separation into structural elements i s nevertheless possible. If the presence of the crosslinks defines the presence of the gel, the zone where the crosslink density (number of w


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crosslinks per unit volume) goes from i t s value i n the gel interior to i t s value, zero, i n the water phase,represents the gel surface, i . e . the interface with the solvent bulk phase. Ideally we could picture this transition as geometrically abrupt, but there i s , i n fact, l i t t l e reality to an i n t e r f a c i a l zone more sharply located than the mean distance between crosslinks in the bulk. The macromolecular fuzz, i . e . the region involving the freely coiling chain segments between crosslinks w i l l also terminate at the interface, and i n part, smooth out the coarse grain of the crosslink density distribution. Even then i t i s most unlikely that the gel surface can be much smoother than the displacements characteristic of the intercrosslink distance. Swelling Equilibrium Since we are considering the open hydrogel-water interface, swelling equilibrium has been established. This means essent i a l l y that the concentration of water i n the gel has been adjusted, by suitably contracting or expanding the distance between crosslinks, by, i n other words, coiling or uncoiling the macromolecular network segment chains, so that solvent chemical potential i s the same inside and out. If this experiment were done using a solution containing a f i n i t e number of unlinked macromolecules i n place of the gel, the system would go to i n f i n i t e dilution. I f , however, the volume of polymer solution were confined inside a closed membrane, which does not permit the polymer component to move out, water w i l l enter, or w i l l tend to enter, the solution space raising the pressure u n t i l the water chemical potential i s matched. Mechanically, this build-up of pressure i s possible because the hydrostatic pressure can be compensated by a stress in the membrane. I f the membrane i s r i g i d (i.e. possesses i n f i n i t e elastic modulus) compensation of forces can be achieved without volume change. In more practical situations the membrane has a f i n i t e elastic modulus, w i l l tend to distend slightly and some swelling w i l l take place. The point to note i s that a real pressure difference i s established between solution and swelling medium and that the water molecules i n the solution phase are "aware" of i t by being forced closer together, i.e. being somewhat more compressed than i n the pure water phase at ambient pressure. In the case of the equilibrium swelling of a gel, the gel material would act as i t s own membrane. The question arises, therefore, whether a hydrostatic pressure difference exists between the interior of the gel and the water phase and whether a pressure gradient accompanies the concentration transition through the interface. This i s a more d i f f i c u l t question to answer than i t should be. F i r s t of a l l the literature i s f u l l of terms which suggest



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t h a t such a pressure a r i s e s . Moreover, mechanical work can be done as a r e s u l t o f s w e l l i n g . Thus s w e l l i n g p r e s s u r e seems t o be an a p p r o p r i a t e term t o apply when one wishes t o c h a r a c t e r i z e the force which would have t o be exerted on the g e l i n order t o prevent i t from s w e l l i n g i n an experiment analogous t o the membrane-polymer s o l u t i o n experiment j u s t d i s c u s s e d . I n t h e l a t t e r case, t o o , one speaks o f a p r e s s u r e , the osmotic p r e s s u r e , which can be t r a n s l a t e d i n t o a r e a l p r e s s u r e e f f e c t when a membrane i s employed t o r e s i s t a change i n volume o f the s o l u t i o n phase, i . e . t o prevent d i l u t i o n . Osmotic pressure i s , however, not an i n h e r e n t mechanical f e a t u r e o f the s o l u t i o n , b u t o n l y a method o f e x p r e s s i n g i t s c o n c e n t r a t i o n . To achieve a r e a l p r e s sure e f f e c t we have t o perform an experiment which w i l l depend upon the presence of a mechanical d e v i c e , t h e membrane, and another phase, t h e pure s o l v e n t . Only then can a p r e s s u r e d i f f e r e n c e be generated, measured and maintained. Now e x a c t l y the same i s t r u e when a g e l i s s t u d i e d under s i m i l a r c o n d i t i o n s . A porous r i g i d support f o r the g e l i s r e q u i r e d . M e c h a n i c a l l y i t i s the e q u i v a l e n t o f t h e membrane i n the osmotic p r e s s u r e experiment. Through i t the g e l i s p u t i n t o contact w i t h the water phase, and by i t s d e v i c e t h e volume o f the g e l i s confined mechanically. P r e c i s e l y as i n the osmotic pressure measurement system, water w i l l tend t o e n t e r , compression of the water molecules w i l l occur, the h y d r o s t a t i c p r e s s u r e w i l l r i s e , and the chemical p o t e n t i a l o f water i n s i d e the compartment w i l l r i s e t o match t h a t o f t h e water o u t s i d e . As i n the case o f osmotic e q u i l i b r i u m , s o l v e n t chemical p o t e n t i a l i s balanced by a r e a l p r e s s u r e r i s e and the mechanical i n t e r a c t i o n between the g e l and i t s porous r i g i d support p r o v i d e s the means by which water compression i s achieved. There i s o n l y one d i f f e r e n c e . The pressure e f f e c t i s not c a l l e d osmotic p r e s s u r e b u t s w e l l i n g pressure. The s i t u a t i o n o f s w e l l i n g p r e s s u r e measurement i s , however, not the s i t u a t i o n o f s w e l l i n g e q u i l i b r i u m . I n t h a t case expans i o n i s u n r e s i s t e d and w i l l stop only when c o n f o r m a t i o n a l changes i n the network segments have so d i s t o r t e d the s t a t i s t i c a l mec h a n i c a l p a r t i t i o n f u n c t i o n o f the system and so d i l u t e d the system t h a t the e f f e c t o f the g e l substance s o l u t e on the s o l v e n t chemical p o t e n t i a l i s reduced t o zero. S o l v e n t chemical p o t e n t i a l i s balanced by changes i n s o l u t e chemical p o t e n t i a l alone and the need f o r a p r e s s u r e r i s e on the s o l u t i o n i s o b v i a t e d . Indeed, i t would be m e c h a n i c a l l y i m p o s s i b l e t o have such a p r e s s u r e a r i s e without a d e v i c e which could compensate t h i s e f f e c t m e c h a n i c a l l y . True enough t h e network i s d i s t e n d e d but there i s no f o r c e i n the network segments a t s w e l l i n g e q u i l i b r i u m . We can c u t such a g e l a t any p o i n t and no volume change w i l l a r i s e . Only then i n c o n t a c t w i t h pure s o l v e n t w i l l f o r c e s a r i s e when the network i s m e c h a n i c a l l y d i s t o r t e d out o f the c o n f i g u r a t i o n i n which i t i s i n thermodynamic e q u i l i b r i u m . Only then w i l l



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i t s segments c a r r y f o r c e . I n contact w i t h a pure s o l v e n t phase, t h e r e f o r e , the c o n f i g u r a t i o n of the network i n i t s s w e l l i n g e q u i l i b r i u m s i t u a t i o n i s the reference unstressed n o n d i s t o r t e d c o n f i g u r a t i o n . Out o f contact w i t h pure s o l v e n t , the g e l w i l l have been synthesized,or formed i n other ways, a t a c o n c e n t r a t i o n above s w e l l i n g e q u i l i b r i u m . For volume p r e s e r v i n g deformations from t h i s s t a t e the system w i l l tend t o r e t u r n t o i t as i t s then reference s t a t e , but only i f out of contact w i t h s o l v e n t . The reference s t a t e of the system i s thus the e q u i l i b r i u m s t a t e of the system under the environmental c o n s t r a i n t s imposed. I t has nothing t o do w i t h whether or not the degree of c o i l i n g of the network segments by chance corresponds t o the conformational d i s t r i b u t i o n o f t h a t polymer species i n f r e e s o l u t i o n . We can, moreover, change the reference s t a t e by changing the o u t s i d e medium. I f , f o r example, as o u t s i d e medium, an aqueous s o l u t i o n were used where s o l u t e molecules are polymers too b i g t o enter the g e l , a d i f f e r e n t s w e l l i n g e q u i l i b r i u m would be reached and the reference s t a t e would correspond t o t h a t s i t u a t i o n . Hence any s t a t e can be a reference s t a t e , but the o u t s i d e medium may have t o possess r a t h e r s p e c i a l p r o p e r t i e s i n each case. I t i s the approach used by F l o r y i n h i s treatment of the i s o l a t e d macromolecule (3). Here the macromolecule i s considered as a microscopic g e l p a r t i c l e and s w e l l i n g t o e q u i l i b r i u m i s allowed t o occur. The s w o l l e n s t a t e of the macromolecule and not i t s Gaussian d i s t r i b u t i o n s t a t e i s now the normal conforma t i o n a l d i s t r i b u t i o n o f the segments i n t h a t s o l v e n t medium. Segment D i s t r i b u t i o n i n the I n t e r f a c e The s w e l l i n g of the macroscopic g e l can thus be considered analogously t o the F l o r y approach. The p r i n c i p a l d i f f e r e n c e d e r i v e s from the f a c t t h a t the segment d i s t r i b u t i o n i s r a t h e r d i f f e r e n t t o s t a r t w i t h . S w e l l i n g w i l l occur i n most cases of good s o l v e n t s and the θ-conditions of i d e a l i n s o l u b i l i t y w i l l not be d i f f e r e n t s i n c e the θ-point corresponds, as b e f o r e , t o the v a n i s h i n g of the second v i r i a l c o e f f i c i e n t i . e . t o the t r a n s i t i o n t o c r i t i c a l l y a t t r a c t i v e polymer-polymer i n t e r a c t i o n s . While we can assume t h a t network segment d i s t r i b u t i o n i n s i d e the g e l i s i s o t r o p i c t h i s d i s t r i b u t i o n goes t o zero over some i n t e r f a c i a l r e g i o n of a s l a b t h i c k n e s s corresponding approximately t o the i n t e r c r o s s l i n k d i s t a n c e . A number of problems a r e , however, here encountered. The d i s t r i b u t i o n of conformations o f a network segment between f i x e d c r o s s l i n k s , a l l o w i n g f o r the e x c l u s i o n of conformations due t o the simultaneous presence of other such network segments, i s not adequately known. S i m i l a r l y , the d i s t r i b u t i o n o f dangling chain ends from the outermost l a y e r o f c r o s s l i n k p o i n t s ( t a k i n g i n t o account t h a t here too there are network segments going



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from these c r o s s l i n k s t o i n t e r i o r c r o s s l i n k p o i n t s and w i l l i n h i b i t conformational freedom) has not y e t been d e r i v e d . I t may be assumed t h a t t h i s d i s t r i b u t i o n has some s i m i l a r i t y t o t h e d i s t r i b u t i o n o f chains t e r m i n a l l y attached t o a r i g i d plane surface (4). Account w i l l , however, have t o be taken o f the f a c t t h a t the outermost l a y e r o f c r o s s l i n k s does not l i e i n one plane and t h a t t h e dangling c h a i n ends are not uniform i n length. We may expect, t h e r e f o r e , t h a t the outermost l a y e r o f a g e l surface i s much t h i c k e r than one i n t e r c r o s s l i n k d i s t a n c e and t h a t the s u r f a c e phase w i l l thus be much more d i f f u s e than the i n t e r i o r s i t u a t i o n o f the g e l . I t should be noted t h a t using θ-conditions f o r the s w e l l i n g w i l l give cases where c h a i n s t a t i s t i c s most c l o s e l y approach the i d e a l Gaussian random walk. R e l a t i o n s h i p between Bulk and Surface S t r u c t u r e Laser s c a t t e r i n g r e s u l t s from g e l s ( 5 , 6 ) and some recent p e r m e a b i l i t y s t u d i e s ( 7 ) both confirm the i d e a t h a t the i n t e r n a l s t r u c t u r e o f g e l s does not n e c e s s a r i l y conform t o the simple con cept t h a t each c r o s s l i n k molecule i n c o r p o r a t e d i n t o the network s t r u c t u r e produces one independent c r o s s l i n k . Many such l i n k s apparently are wasted simply producing l a r g e r c h a i n s . Others occur t o o c l o s e t o each other and may only serve t o extend t h e r e g i o n which mechanically w i l l a c t as a s i n g l e c r o s s l i n k , a l l chemical c r o s s l i n k s i n t h a t r e g i o n a c t i n g as one. Hence many g e l s r e a c t as though they had f a r fewer e f f e c t i v e c r o s s l i n k s than apparently i n c o r p o r a t e d and as though they had much wider openings i n them than would be suspected from the amount o f gel substance present. E f f e c t s l i k e these, a coarsening o f the g r a i n o f the g e l , may a l s o be expected t o a f f e c t the surface zone commensurately. Hydrodynamic E f f e c t s Macromolecules, p h y s i c a l l y adsorbed o r c h e m i c a l l y attached (at one or two p o i n t s ) t o s o l i d support surfaces produce a d i f f u s e macromolecular zone. I n attempts t o measure the t h i c k ness of such l a y e r s by the change i n dimensions they produce, i t i s found t h a t the t h i c k n e s s e s so measured are e f f e c t i v e l y much l a r g e r than those determined by other methods (9/10). There i s thus a hydrodynamic e f f e c t which produces an e x t r a energy d i s s i p a t i o n i n the f l u i d l a y e r s a d j o i n i n g t h e macro molecular s u r f a c e . Confirmation t h a t flow p a s t a g e l , o r g e l - l i k e , s u r f a c e i s a s s o c i a t e d w i t h an e x t r a energy d i s s i p a t i o n was obtained from s t u d i e s o f the r e s i s t a n c e t o flow through c y l i n d r i c a l


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channels i n a gel {11) . Compared with channels of the same dimensions with r i g i d walls, the cylinder i n the gel allows only a reduced throughput. The effect could be correlated with the elastic modulus of the gel and the thickness of the gel layer. I t seems to be due to oscillations excited i n the interface ( 1 2 ) . It i s to be hoped that the interesting properties of the hydrogel surface which have led to an increasing number of applications i n a variety of fields w i l l also stimulate more systematic work on their physico-chemical and mechanical attributes.

Literature Cited: 1. Holly F.J. and Refojo M.F. Polymer Preprints (1975) 16(2) 426. 2. Silberberg A. Polymer Preprints (1970) 11, 1289. 3. Flory P.J. "Principles of Polymer Chemistry" (1953) Cornell Univ.Press, Ithaca, p.519. 4. Hesselink F.Th. J.Phys.Chem. (1971) 75, 65. 5. Dusek K. and Prins W. Adv.Polymer Sci. (1969) 6, 1-102. 6. Pines E. and Prins W. Macromolecules (1973) 6, 888. 7. Weiss N. and Silberberg A. Biorheology (1975) 12, 107. 8. Weiss N. and Silberberg A. This book. 9. Priel Z. and Silberberg A. Polymer Preprints (1970) 11, 1405. 10. Silberberg A. "Colloques Internationaux du C.N.R.S. No. 233 (1975) p.81. 11. Lahav J., Eliezer N. and Silberberg A. Biorheology (1973) 10, 595. 12. Hansen R.J. and Hunston D.L. J.Sound and Vibration (1974) 34, 297.


Hydrogels for Medical and Related Applications

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