Supporting Information

Size: px

Start display at page:

Download "Supporting Information"

Jeremy Stephens
6 years ago
Views:

1 Supportig Iformatio Reversible Vesicle Spherical Micelle Trasitio i a Polyio Complex Micellar System Iduced by Chagig the Mixig Ratio of Copolymer Compoets Ritaro Takahashi, Takahiro Sato, * Ke Terao, Shi-ichi Yusa Departmet of Macromolecular Sciece, Osaka Uiversity, 1-1 Machikaeyama-cho, Toyoaka, Osaka , Japa Departmet of Applied Chemistry, Graduate School of Egieerig, Uiversity of Hyogo, 167 Shosha, Himeji, Hyogo , Japa *(T.S. tsato@chem.sci.osaka-u,ac.jp Compositio of the Polyio-Complex Solutio. Let us cosider a mixture of a polyaio ad a polycatio dissolved i aqueous solutio. Here, the polyaio ad polycatio are assumed to cosist of A ad M + repeatig uits with ui-valet egative ad positive charges, respectively, ad the molar cocetratios of the A ad M + repeatig uits i the solutio are deoted as C 0 ad C 0+, respectively. By the strog electrostatic attractio, A ad M + form a eutral complex AM: K a A + M +!!!!! AM (S1 where K a is the associatio costat. Thus, we regard the polyio mixture solutio as a quaterary system of A, M +, AM, ad the solvet. (Here, the aqueous salt is regarded as a

2 sigle solvet compoet. Sice the eutral complex AM has o et charges, its solubility to the aqueous medium should be much lower tha A or M +, ad a liquid-liquid phase separatio may take place i the solutio. The compositios of the coexistig dilute ad cocetrated phases are specified i terms of the molar cocetratios of A (C (d 0, C + (C (d 0+, ad AC (C (d 0± i the dilute phase, ad of A (C 0, C + (C 0+, ad AC (C 0± i the cocetrated phase. Accordig to the law of mass actio, we have the followig relatios amog the molar cocetratios: C (d 0± = K a C (d (d 0 C 0+ C 0± = K a C 0 C 0+ The mass coservatio rule gives us the relatios: ( + ± ( 1 ( + ± ( ( 1 ( C = C + C Φ + C + C Φ C C C C C (d (d (d (d 0 = 0 + 0± Φ ± Φ where Φ is the volume fractio of the cocetrated phase i the solutio. (S (S3 I additio to these equatios, the phase equilibrium coditios with respect to the chemical potetials µ of the three compoets must be fulfilled µ (d = µ, µ + (d = µ +, µ ± (d = µ ± (S4 I priciple, the six molar cocetratios plus Φ ca be determied by the above seve simultaeous equatios. However, due to the lack of precise expressios of the chemical potetials, it is practically impossible to determie the compositio from the above equatios. We use the followig pheomeological equatios, istead of eqs S4, to determie the six molar cocetratios ad Φ. First, the eutral complex AM is assumed to be so hydrophobic that the dilute phase does ot cotai AM, i.e.,

3 C 0± (d = 0 (S5 If the cocetrated phase is dispersed as colloidal particles i the solutio, we ca determie from the scatterig experimet the polymer mass cocetratio c i the cocetrated phase, which is related to C 0, C 0+, ad C 0± by ( ± c = M C + M C + M + M C (S6 where M 0+ ad M 0 are the molar masses of the polycatio ad polyaio repeatig uits, respectively (icludig the couter ios. Furthermore, from the electrophoretic light scatterig (ELS result, we ca obtai the et charge c of the colloidal droplet of the cocetrated phase (i the uit of the elemetary charge, which ca be related to C 0 ad C 0+ by ( + M c = C 0 C0 (S7 c where M is the molar mass of the colloidal droplet of the cocetrated phase, which ca be determied from the scatterig experimet. Eqs S5 S7, istead of eqs S4, are used to calculate the six molar cocetratios. The x + depedece of c may be writte as M c = ξ ( x x + + (S8 c where ξ ad x + are parameters determied experimetally.; the latter parameter x + is x + where the zeta potetial of the cocetrated-phase droplet becomes zero. From eqs S, S3, ad S5 S8, we ca obtai the relatios ± = + a ± a + 4 a + ξ ( + + C a K ak K x x 1 0+ = ξ a 0± + ξ + + C ( x x K C ( x x 1 0 = ξ a 0± ξ + + C ( x x K C ( x x (S9

4 with parameter a defied by ( ξ c M M ( x x a M + M 0+ 0 (S10 I the right-had side of the equatio for C 0± i eq S9, the double sig idicates plus at x + > x + ad mius at x + < x +. Because the electrostatic attractio betwee A ad M + is strog, we ca approximate K a to be ifiity. Usig this approximatio, we obtai from eqs S9 C 0± ξ c M x x = M + M 0+ 0 (S11 C ( ( 0 ( ξ x+ x+ x+ x+ x+ x+ 0+ =, C 0 = x+ < x+ ξ x+ x+ x+ < x+ 0 ( ( ( (S1 If x + = 1/, the major compoet i the dilute phase is A at x + < 1/ ad M + at x + > 1/. However, if x + > 1/, the coversio of the major compoet i the dilute phase occurs at x + = x + (d < 1/, ad if x + < 1/, it occurs at x + = x + (d > 1/. The coversio mixig ratio x + (d i the dilute phase ca be calculated by x (d + ( ( Mx+ M x+ Mx+ ξ, M Ξ M C0± + C0+ 1+Ξ 1 Ξ 1 + Ξ = Ξ (S13 As i the case of the cocetrated phase, we eglect the mior compoet i the dilute phase, i.e., C 0 (d = 0 at x + > x + (d ad C 0+ (d = 0 x + < x + (d. Usig eqs S3, S5, ad S1, we obtai the followig equatios. 0 (d c, 0+ C0± + C0 ( 0 0 C C0+ C0 C + C Φc Φ = C = x > x 1 Φ 0+ (d c, 0 C0± + C0+ c ( 0 0 c (d ( + + C C0 C0+ + C + C Φc Φ = C = x < x 1 Φ (d ( + + (S14a (S14b

5 Cotrast Factors. The optical costat K e is defied by K e NAae γ av = (S15 with the Avogadro costat N A, the classical radius of electro a e, ad the average cotrast factor γ av of the polymers. For the mixture of the AP ad MP copolymers i aqueous NaCl solutio, γ av was calculated by γ γ w + γ w (S16 av MP MP AP AP where w MP ad w AP are the weight fractios of the copolymers MP ad AP i the solutio, respectively, ad γ MP ad γ AP are their cotrast factors, calculated by γ MP ( + ( + M0+ N0+ + M0N0 M0 N0 + M0N, γ 0 ( + AP ( M0+ N0+ + M0N0 M0 N0 + M0N0 γ γ γ γ = = with γ i (i = +,, defied by (S17 υ γ i ( 1 w + M M M e0i i e,ho e,nacl NaCl 0i υsolv HO NaCl w NaCl (S18 Here e0i, e,h O, ad e,nacl are umbers of electros of the moomer uit i (icludig the couterio, H O molecule, ad NaCl, respectively, M 0i, M H O, ad M NaCl are molar masses of the moomer uit i, H O, ad NaCl, respectively, υ i is the partial specific volume of the moomer uit i, υ solv is the specific volume of the solvet (water cotaiig 0.1 M NaCl, ad w NaCl is the weight fractio of NaCl i the solvet. The mixture of MP ad AP forms the polyio complex micelle, of which hydrophobic core cosists of the moomer uits M + ad A as well as the eutral complex AM (see above. The molar cocetratios of M +, A, ad AM i the hydrophobic core are C 0+, C 0, ad C 0±, respectively, as discussed above. The cotrast factor γ mic of the micelle is give by

6 γ ( ʹ ʹ ( ʹ ʹ γ± M0+ + M0 C0± + γ+ M0+ C0+ + γ M0 C0 core = M0+ + M0 C0± + M0+ C0+ + M0 C0 (S19 where M 0+ ad M 0 are the molar masses of M + ad A ios, respectively (without the couterios, ad γ ± is the cotrast factor of the eutral complex AM calculated by γ ± e0 ʹ e,ho + + e0 ʹ M0+ υ+ + M0 υ MNaClυ NaCl e,nacl ( 1 wnacl + wnacl (S0 M0ʹ+ + M0ʹ ( M0ʹ+ + M0ʹ υsolv MHO MNaCl with the umbers of electros e0+,ad e0,of the moomer uit ios i (without the couterio ad the specific volume υ NaCl of NaCl. Scatterig Fuctios of Micelles. Whe the complex of AP ad MP forms a sigle bilayer vesicle, the particle scatterig fuctio (or the itra-particle iterferece factor P M (k with the molar mass M is give by 1, ( D D 1 PM( k = γ MPM, D( kexp dd (S1 πσd σ D where P M,D (k is the particle scatterig fuctio of the vesicle with the molar mass M ad the thickess of the hydrophobic core D, ad D ad σ D are the mea value ad variace of the thickess of the hydrophobic core, respectively. If the shell part is represeted as a assembly of Gaussia chais, the scatterig fuctio P M,D (k is give by γ R 3 P M,D (k = γ core W out Φ(kR out R 3 i Φ(kR i core +γ 3 W shell A coroa,ves (k R i W +γ shell m 3 R out Ω(k S A coroa,ves (k (S with Φ(x 3(si x xcos x x 3 (S3

7 A coroa,ves (k = 1 exp( k S si[k(r + S out k S k(r out + S 1/ 1/ ] + si[k(r S i k(r i S 1/ 1/ ] (S4 [ x + x] exp( 1 Ω( x (S5 x ( C0+ + C0± N0+ + ( C0 + C0± N0 0+ ( ± + 0 ( 0 + 0± m = M M C C M C C (S6 I those equatios, S deotes the square radius of gyratio of the coroal chai, ad R i ad R out are the ier ad outer radii of the hydrophobic core, respectively. The weight fractios of the core ad shell parts i the micelle are give by W = 1 W = M0ʹ+ ( C0+ + C0± + M0ʹ ( C0 + C0± ( MMP ʹ N0+ ( C0+ + C0± + ( MAP ʹ N0 ( C0 + C0± core shell (S7 where M MP ad M AP are the molar masses of the polycatio ad polyaio block chais without the couterios, respectively. Usig the mass cocetratio c core of the hydrophobic core, the molar mass of the vesicle M, the hydrophobic core thickess D, ad W core, R i ad R out are give by D D D MW 1 R = R R = R+ R (S8 3 core i, out, 3 π NAccoreD The adjustable parameters to calculate P M (k for the vesicle are c core, S, D, ad σ D. I the case that eutral complex is a sphere micelle, P (k is give by 1, M = core coreφ core + shell coroa,sph γ P ( k γ W ( kr γ W A ( k Wshell coroa,sph m + γ Ω ( k S A ( k (S9 A coroa,sph (k = 1 exp( k S k S si[k(r + S core 1/ ] k(r core + S 1/ (S30

8 where R c is radius of the hydrophobic calculated from the mass cocetratio c core of the hydrophobic core by R core 3MWcore = 4π NAccore 1/3 (S31 The polymer mass cocetratio c coroa i the coroal regio calculated by c coroa mm w,1 8πN ARcore S = mm 8πN A( Ri + R 1/ w,1 out S 1/ (spherical micelle (vesicle (S3 where the thickess of the coroal regio is approximated by S 1/. We did ot cosider the iterfacial thickess betwee the core (or shell ad coroal regios. Electrostatic Eergy of Charged Micelles. Let us cosider the vesicle with the uiformly charged hydrophobic core of the outer ad ier radius R out ad R i ad with the charge Q ves, immersed i the aqueous solutio with the Debye legth κ 1 (= (8πN A QC S 1/, where N A is the Avogadro costat ad Q is the Bjerrum legth. Accordig to the Gauss law, the electrostatic eergies outside (r > R out ad withi (R i < r < R out the charged hydrophobic core are give by U out = Q ves ( 1+ 1 κ R out exp( κ R out ( (S33 8πεR out 1+κ R out U 6 3 ( R R ( R R ( R R Qves out i out i out i core = 40πε R 3 out ( Rout Ri respectively, with the dielectric costat ε of the solvet water. (S34 I eq S33, we have approximated κ 1 i the outside coroal regio to be equal to that i the outside the coroal regio. Furthermore, eglectig couterios of the charged core withi the ier coroal

The electrostatic eergies outside (r > Rcore ad withi (0 < r < Rcore the charged hydrophobic core are give by eqs S33 ad S34 where Qves, Rout, ad Ri are replaced by Qsph, Rcore, ad 0, respectively.

9 ad solvet regio of the vesicle, we have the total electrostatic eergy of the vesicle Uves by eq 11 i the text. The electrostatic eergy of the spherical micelle with the uiformly charged hydrophobic core of the radius Rcore ad with the charge Qsph, immersed i the aqueous solutio ca be calculated similarly. The electrostatic eergies outside (r > Rcore ad withi (0 < r < Rcore the charged hydrophobic core are give by eqs S33 ad S34 where Qves, Rout, ad Ri are replaced by Qsph, Rcore, ad 0, respectively. The total electrostatic eergy of the spherical micelle Usph by eq 10 i the text. Trasmittace Electro Microscopy (TEM. The test solutios for TEM were prepared by MP AP procedure (cf. experimetal sectio. placed o a copper grid coated with Formvar film. A drop of each solutio was The sample was staied by a aqueous solutio of sodium phosphotugstate (0.wt%, dried i vacuo, ad the observed usig a JEM-100 trasmittace electro microscope (JEOL Ltd., Tokyo. (a (b 100 m Figure S m TEM images of MP AP mixtures at x+ = 0.4 (a ad 0.8 (b. Figure S1 shows TEM images of particles formed by AP MP mixtures at x+ = 0.4. I both images, spherical objects are observed. The shape ad radius (~ 0 m agree with

the SAXS results, supportig the formatio of the spherical micelle. A part of the spherical objects secodarily aggregate, which probably take place i dryig for the sample preparatio.

10 the SAXS results, supportig the formatio of the spherical micelle. A part of the spherical objects secodarily aggregate, which probably take place i dryig for the sample preparatio. I the case of x + = 0.6, larger spherical objects are observed, give elsewhere. 3 Note that such larger spherical objects observed at x + = 0.6 were ever foud at x + = 0.4 ad 0.8. Dyamic Light Scatterig (DLS. DLS measuremets were performed usig a ALV/DLS/SLS-5000 light scatterig photometer at 5 C. A vertically polarized YAG laser (wavelegth: 53 m was used as icidet light. Each test solutios, prepared i the same maer as reversibility ivestigatio usig SAXS, was diluted with 0.1 M aqueous NaCl solutio to adjust the polymer cocetratio c = g/cm 3 for trasparecy, ad poured ito a quartz cell. g ( (t x AP +MP MP +AP k B T/(6πη 0 k t / m

11 Figure S. Auto-correlatio fuctios at the scatterig agle of 90 for the polyio complex micelle formed of AP ad MP i aqueous NaCl solutio, plotted agaist k B T/(6πη 0 k t. Gree circle with upward bar: x = 0.6 prepared by MP AP, blue circle: x = 0.4 prepared by addig AP solutio ito the solutio of x = 0.6, red circle with dowward bar: x = 0.6 prepared by addig MP solutio ito the solutio of x = 0.4, orage circle: x = 0.8 prepared by addig MP solutio ito the solutio of x = 0.6, purple circle: x = 0.6 prepared by addig AP solutio ito the solutio of x = 0.8. The three scatterig fuctios of x (gree, red, ad purple circles are overlapped. Solid curves idicate results of the sigle expoetial fittig. Figure S compares the auto-correlatio fuctios g ( (t 1 plotted agaist k B T/(6πη 0 k t (k B is the Boltzma costat, T is the absolute temperature, ad η 0 is the viscosity coefficiet of the solvet at x + = 0.6, 0.4, ad 0.8. Here, the test solutios of x + = 0.4 ad 0.8 were prepared from the solutio of x + = 0.6 by addig AP or MP solutio. The scatterig from the free sigle chai was so weak ad ot observed eve at x + = 0.4 ad 0.8. Therefore, the scatterig compoets at x + = 0.6 is assiged to the vesicle, ad those at x + = 0.4 ad 0.8 are to the spherical micelle split from the vesicle. The g ( (t for the spherical micelle at x + = 0.4 ad 0.8 ca be almost fitted by sigle expoetial decay fuctios (solid curves i the Figure, idicatig arrow distributio ad beig cosistet with the results of the SAXS profile fittig (cf. Table. Whe MP or AP solutio was added ito the solutio of x + = 0.4 ad 0.8 to recover x + to be 0.6 agai, the g ( (t almost completely recover to the g ( (t of the origial solutio of x + = 0.6. Therefore, the size ad size distributio of the vesicle are reproducible.

12 Referece 1. Pederse, J. S.; Gersteberg, M. C., Scatterig Form Factor of Block Copolymer Micelles. Macromolecules 1996, 9, Pederse, J. S., Aalysis of small-agle scatterig data from colloidsad polymer solutios: modelig ad least-squares fittig. Adv. Colloid It. Sci. 1997, 70, Takahashi, R.; Sato. T.; Terao, K.; Yusa, S., Itermolecular Iteractios ad Self-Assembly i Aqueous Solutio of a Mixture of Aioic Neutral ad Catioic Neutral Block Copolymers. Macromolecules 015, 48, 7 79.

J. Serb. Chem. Soc. 82 (4) S208 S220 (2017) Supplementary material

J. Serb. Chem. Soc. 82 (4) S208 S220 (2017) Supplementary material J. Serb. Chem. Soc. 82 (4) S8 S2 (7) Supplemetary material SUPPLEMENARY MAERIAL O Experimetal measuremets ad modellig of solvet activity ad surface tesio of biary mixtures of poly(viyl pyrrolidoe) i water