Selection between block- and homo-polyelectrolytes through polyion complex formation in aqueous medium

Abstract

A strict selection of an oppositely charged pair of block-polyelectrolytes, consisting of ionic and non-ionic hydrophilic blocks, was found to occur in aqueous medium upon the addition of poly(ethylene glycol)-b-poly(α,β-aspartic acid) [PEG–P(Asp)] (anionic block-polyelectrolyte) solution into a mixed solution of PEG-b-poly(L-lysine) [PEG–P(Lys)] (cationic block-polyelectrolyte) and P(Lys) (homo-polyelectrolyte), leading to the formation of polyion complex (PIC) micelles exclusively composed of block-polyelectrolytes pairs. The selection process seems to proceed under the condition of dynamic equilibrium, because the addition of a stoichiometric amount of PEG–P(Lys) to a solution of PIC micelles composed of PEG–P(Asp) and P(Lys) resulted in nearly complete (96%) replacement of P(Lys) with PEG–P(Lys) in the micelles. This phenomenon may be explained by assuming the increased association force of block-polyelectrolytes compared with homo-polyelectrolyte, presumably due to the frustrated conformation of block-polyelectrolytes composed of incompatible segments, such as PEG and polyelectrolyte, in aqueous medium. An increase in the association force of block-polyelectrolytes was also supported by the formation of non-stoichiometric PIC associates in the range in which the block-polyelectrolyte comprises a major component in the medium ([Lys] < [Asp]); in this range, all of the PEG–P(Asp) strands behave as host molecules to participate in the complexation with P(Lys) strands as guest molecules, leaving no free PEG–P(Asp) strands in the medium. Alternatively, P(Lys) strands seem to always behave as guest molecules to form stoichiometric PIC micelles with PEG–P(Asp), even when they exist as a major component ([Lys] > [Asp]), leaving excess P(Lys) strands in the free form in the medium. This new mode of molecular recognition based on polymer architecture discovered here may be integrated into various molecular systems to exert dynamic functions with environmental sensitivity.

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1. Introduction

Polyion complex formation represents an interesting principle for self-organizing supramolecular structures and has gained high practical relevance as layer-by-layer coatings, membranes with special separation properties and for microencapsulation.^1–6 Nevertheless, simple mixing of oppositely charged polyelectrolyte solutions leads to spontaneous aggregation, being difficult to control the size and colloidal stability. The use of block-polyelectrolytes composed of charged and non-ionic segments for polyion complexation is an effective approach to control the complexation process, including size modulation and increased colloidal stability. Our previous study revealed that the mixing of a pair of oppositely charged block-polyelectrolytes led to the formation of core–shell-type polyion complex (PIC) micelles characterized by a distinct core–shell structure, in which the polyion complex core is surrounded by a shell of tethered non-ionic segments.⁷ PIC micelles form not only from pairs of oppositely charged block-polyelectrolytes, but also from mixtures of block-polyelectrolytes and oppositely charged compounds, for example, synthetic and natural polyelectrolytes, surfactants, and biologically relevant molecules, including nucleic acid derivatives and enzymes.^8–15 PIC micelles entrapping biologically relevant molecules have received considerable attention from applied fields for their potential use in nanometric-scaled bioreactors and as nanocarriers in drug and gene delivery.^8,9 A unique feature of PIC micelle formation from the viewpoint of supramolecular chemistry is that the clear chain-length recognition occurs in the process of micellization from the pair of oppositely charged block-polyelectrolytes, poly(ethylene glycol)-b-poly(L-lysine) [PEG–P(Lys)] and poly(ethylene glycol)-b-poly(α,β-aspartic acid) [PEG–P(Asp)].¹⁶ This unique chain-length recognition is driven by the requirement for charge stoichiometry with the uniform distribution of ion pairs in the core, without phase mixing with the PEG shell, demanding the strict alignment of the molecular junction of two segments of the block-polyelectrolytes at the core–shell interface.

Here, we report another type of molecular recognition found in the process of PIC micelle formation from block-polyelectrolytes. Strict selection of oppositely charged pairs of PEG-based block-polyelectrolytes, excluding the pairing of block- and homo-polyelectrolytes, occurred in aqueous medium upon the addition of PEG–P(Asp) (anionic block-polyelectrolyte) solution into a mixed solution of PEG–P(Lys) (cationic block-polylectrolyte) and poly(L-lysine) [P(Lys)] (cationic homo-polyelectrolyte), leading to the formation of polyion complex (PIC) micelles exclusively composed of block-polyelectrolyte pairs. This newly identified phenomenon of molecular recognition in a system composed of flexible and coiled polymer strands may provide insight for constructing supramolecular associates with characteristic architecture and functionality.

2. Materials and methods

2.1. Materials

Poly(ethylene glycol)-b-poly(α,β-aspartic acid) [PEG–P(Asp); PEG M_w = 5000 g mol⁻¹] with different polymerization degrees (PD) of P(Asp) segments (18 and 78; the code names are AB18 and AB78, respectively), poly(ethylene glycol)-b-poly(L-lysine) [PEG–P(Lys); PEG M_w = 5000 g mol⁻¹] with different PD of P(Lys) segments (18 and 78; the code names are CB18 and CB78, respectively) and poly(L-lysine) [P(Lys)] with different PD (20 and 82; the code names are CH20 and CH82, respectively) were synthesized by ring-opening polymerization of the N-carboxy anhydrides of β-benzyl-L-aspartate or ε-benzyloxycarbonyl-L-lysine, as described previously.^7,17

2.2. Preparation of PIC micelle solutions

Appropriate amounts of PEG–P(Asp), PEG–P(Lys) and P(Lys) were separately dissolved in sodium phosphate buffer (PBS: pH 7.4; 10 mM; Na₂HPO₄·12H₂O 2.865 g L⁻¹, NaH₂PO₄·2H₂O 0.312 g L⁻¹). The resulting solutions were passed through a 0.1 μm filter. PEG–P(Asp) solution was added to the catiomer (PEG–P(Lys) or P(Lys) or their mixture) solution at various mixing charge ratios. For the experiment evaluating stoichiometry, an appropriate volume of buffer was added to the mixture to maintain constant concentration of either anionic or cationic polyelectrolytes. The prepared sample solutions were stored overnight before evaluation.

2.3. Gel-filtration chromatography

Gel-filtration chromatography (GFC) measurements were carried out in 10 mM sodium phosphate buffer with 50 mM NaCl (pH 7.4) as an eluent, using a column combination of Superdex 75 HR (Amersham Pharmacia Biotech, Sweden) and TSK gel G3000PW_XL (Tosoh Co., Tokyo, Japan). The flow rate was 0.3 mL min⁻¹, and the difference in refractive index was detected at room temperature.

2.4. Viscosity measurements

Viscosity measurements were carried out using a Cannon–Fenske viscometer (Shibata Scientific Technology, Ltd). Solutions of PEG–P(Lys)/PEG–P(Asp) or P(Lys)/PEG–P(Asp) were prepared at various charge ratios keeping the total polymer concentration constant (2.0 mg mL⁻¹). Solution flow times were measured at 25 °C, and the average flow time was calculated from triplicate measurements. Kinematic viscosity (η) was calculated using the following equation:

(kinematic viscosity) = (constant of viscometer) × (flow time)

The kinematic viscosity of sodium phosphate buffer (η₀) was also measured to calculate the relative viscosity (η/η₀).

2.5. Light scattering measurements

Dynamic and static light scattering measurements were carried out using a DLS-7000 spectrophotometer (Otsuka Electronics Co., Ltd, Osaka, Japan). Vertically polarized light of 488 nm from an Ar ion laser (75 mW) was used as an incident beam. All measurements were carried out at 25.0 ± 0.2 °C. Dynamic light scattering measurements were carried out at detection angle of 90°, and the average diameter and polydispersity index were then determined using a cumulant method. Static light scattering measurements were carried out for solutions with concentrations of 1.0, 2.0, 3.0 and 4.0 mg mL, at detection angles of 40° to 150° per 10°, and Zimm plots were prepared. Increments of the refractive index, dn/dc, of solutions were measured using a DRM-1020 double-beam differential refractometer (Otsuka Electronics Co., Ltd, Osaka, Japan).

2.6. Analytical ultracentrifugation measurements

Analytical ultracentrifugation measurements were carried out using an Optima XL-A analytical ultracentrifuge (Beckman Coulter Inc.).¹⁸ The sedimentation velocity of the mixture of P(Lys) and PEG–P(Asp) at an angular velocity of 40 000 rpm was detected using Rayleigh interference optics at 25 °C. The sedimentation profiles were obtained from the movement of the boundary in sedimentation velocity experiments with mixtures of P(Lys) and PEG–P(Asp).

3. Results and discussion

3.1. Selective PIC micelle formation from block-polyelectrolytes pair in the presence of homo-polyelectrolytes

A mixed solution of PEG–P(Lys) (CB78) and P(Lys) (CH82) containing an equal residual molar ratio of Lys units was prepared in PBS, and added to the PBS solution of PEG–P(Asp) (AB78) at varying concentrations to examine the selective paring in the process of PIC micelle formation from GFC measurements. The resulting GFC chromatograms are shown in Fig. 1. Note that PEG–P(Lys) (CB78) and P(Lys) (CH82) in the initial solution separately eluted at elution volumes of 17.1 and 19.9 mL, respectively ([Asp]/[Lys] = 0). CB78 had a larger peak area than CH82 due to the additional contribution of the PEG segment to the refractive index. The addition of PEG–P(Asp) led to the appearance of a new peak corresponding to PIC micelles at an elution volume of 13.1 mL, with a gradual increase in the peak area resulting from increasing the relative amount of PEG–P(Asp) in the mixture. Notably, the decrease in the peak area in the region of 0 < [Asp]/[Lys] < 0.5 occurred only for CB78, while the peak area of CH82 remained constant. This result clearly indicates the exclusive pairing of block-polyelectrolytes to form PIC micelles without any involvement of CH82, the cationic homo-polyelectrolyte, in the process. Micellization of CH82 with AB78 started to occur when [Asp]/[Lys] exceeded 0.5, after the total consumption of free CB78 in the milieu. This profile is more clearly seen in Fig. 2, demonstrating the change in the relative peak areas (A/A₀) [= (the peak area at each [Asp]/[Lys])/(peak area at [Asp]/[Lys] = 0)] of CB78 and CH82, with [Asp]/[Lys]. Obviously, at 0 < [Asp]/[Lys] < 0.5, CB78 selectively decreased in proportion to [Asp]/[Lys], with A/A₀ of CH82 remaining constant, indicating selective recognition between pairs of oppositely charged block-polyelectrolytes. The association of CH82 with AB78 occurred after the total consumption of CB78 in the system for the formation of PIC micelles of AB78/CH82. By comparing the initial slope of changes in A/A₀ of CB78 and CH82 in Fig. 2, AB78 was calculated to select CB78 from the cationic polyelectrolyte mixture with 95% purity. This result indeed clearly indicates that the anionic block-polyelectrolyte (AB78) selects the cationic block-polyelectrolyte (CB78) in an essentially exclusive manner to form PIC micelles.

Fig. 1 Gel-filtration chromatographs for mixtures of PEG–P(Asp) (AB78), PEG–P(Lys) (CB78) and P(Lys) (CH82) at various mixing ratios.

Fig. 2 The relative peak areas (A/A₀) of CB78 (●) and CH82 (○) at varying [Asp]/[Lys] in mixtures of AB78, CB78, and CH82. A/A₀ was calculated from the GFC charts shown in Fig. 1.

3.2. Stoichiometry of PIC micelle formation

To further explore PIC micellization in AB/CB (block-block) and AB/CH (block-homo) systems, the stoichiometry was evaluated from relative viscosity measurements. Fig. 3(a) shows the change in relative viscosity (η/η₀) with the residual molar ratio of charged monomer units. Both AB/CB and AB/CH systems showed minimal η/η₀ at the stoichiometric point ([Lys] = [Asp]), consistent with the formation of PIC micelles with stoichiometric composition. The η/η₀ decreased linearly with the residual ratio for AB/CB, approaching the neutralized point in an equal manner either from an excess of AB or CB. Of interest, the AB/CH system apparently revealed a different trend to give an unsymmetrical profile in Fig. 3(a). In particular, the change in η/η₀ with residual molar ratio at [Lys] < [Asp] is less significant than that in other systems, and thus, shows a discontinuity when approaching a stoichiometric composition ([Lys] = [Asp]). Note that such a discontinuous change in η/η₀ at the stoichiometric point was also observed for other combinations of AB and CH with different polyelectrolyte length (AB18/CH20, AB18/CH82, AB78/CH20), indicating that this phenomenon was independent of the length of charged segments (data not shown).

Fig. 3 Change in the relative viscosity (a) and relative scattering intensity (b) with residual molar ratio for PEG–P(Asp)/PEG–P(Lys) (AB78/CB78) (●) and PEG–P(Asp)/P(Lys) (AB78/CH82) (○) systems.

The stoichiometry of PIC micelle formation was also evaluated using light scattering intensity measurements, which is more sensitive to a change in the apparent molecular weight of polymer associates. Fig. 3(b) shows the change in relative scattering intensity (I/I₀), defined as the ratio of scattering intensity at each charge ratio against that at the stoichiometric point ([Lys] = [Asp]), with the residual molar ratio for AB78/CB78 and AB78/CH82 systems. I/I₀ linearly increased toward the stoichiometric point ([Asp] = [Lys]) for AB78/CB78 in all regions and AB78/CH82 in the region of [Asp] < [Lys]. This linear increment indicates cooperative PIC micelle formation, that is, PIC micelles with stoichiometric charge composition and excess polymer in the free form co-exist in these regions, corresponding to each charge ratio. This trend of change in I/I₀ for AB78/CB78 in all regions, and AB78/CH82 in the region of [Asp] < [Lys], is consistent with the results of the change in relative viscosity shown in Fig. 3(a). Alternatively, in a similar manner to the results of the change in relative viscosity shown in Fig. 3(a), the trend of the change in I/I₀ with a residual ratio for AB78/CH82 at [Lys] < [Asp] was different from the others, maintaining very small values throughout this region with a slight increase toward the stoichiometry point.

Cooperative micellization was also supported by dynamic light scattering (DLS) measurements. Fig. 4 shows the change in the cumulant diameter of the PIC micelles and polydispersity index determined by DLS for AB78/CB78 and AB78/CH82 systems. Note that insufficient photon counts for accurate DLS measurements were attained for AB78/CH82 in the region of [Lys] < [Asp], as expected from the result of the scattering intensity measurements in Fig. 3(b). The cumulant diameter of micelles was independent of the residual molar ratio for both AB78/CB78 and AB78/CH82 systems, and maintained constant values of 40 nm and 50 nm, respectively. This constant diameter of micelles, regardless of the mixture composition, is consistent with the scheme of cooperative micellization. The value of the polydispersity index (μ₂/Γ²) never exceeded 0.1, indicating the narrow distribution of the micelles.¹⁹ It should be noted that the polydispersity index gradually decreased approaching the stoichiometric point, reaching a minimum value of 0.02 at the stoichiometric point. This change in polydispersity index might reflect the contribution of free polymer chains in the system, although their contribution to the scattering intensity is significantly smaller than that of PIC micelles with appreciably high molecular weights. It is then reasonable that the polydispersity index would decrease approaching the stoichiometry point, due to the decrease in the amount of the free polymer chains in the solution, assuming the cooperative micellization. It is also worthy to note from the results shown in Fig. 3(b) and Fig. 4 that no multi-molecular micellization occurs with high association number for AB78/CH82 at [Lys] < [Asp], the region with excess anionic block-polyelectrolyte compared to cationic homo-polyelectrolyte. AB78/CH82 in this region revealed 20 times smaller I/I₀ value than AB78/CB78, suggesting that the assumed complexes formed from AB78/CH82 pairs may have a non-cooperative nature with considerably lower molecular weight, i.e. lower association number, than stoichiometric PIC micelles.

Fig. 4 Change in the cumulant diameter (circle) and the polydispersity index (triangle) with residual molar ratio for PEG–P(Asp)/PEG–P(Lys) (AB78/CB78) (closed symbol) and PEG–P(Asp)/P(Lys) (AB78/CH82) (open symbol) systems.

3.3. Non-stoichiometric complex formation from P(Lys) (CH) and PEG–P(Asp) (AB) at [Lys] < [Asp]

The association behavior of AB/CH at [Lys] < [Asp] was further examined for combinations of varying lengths of charged segments (AB18/CH20, AB18/CH82, AB78/CH20, AB78/CH82) to clarify the features of polyion complex formation in non-stoichiometric conditions. Static light scattering measurements were carried out on the AB/CH system at [Lys]/[Asp] = 0.4, 0.6 and 0.8 to determine the apparent weight-averaged molecular weights (M_w,app) from Zimm plots. The obtained M_w,app values are summarized in Table 1 together with the M_w,app values of PIC micelles prepared in the charge stoichiometric condition.

Table 1 SLS data for mixtures of PEG-P(Asp) (AB) and P(Lys) (CH) at various charge ratios.

Aniomer	Catiomer	[Lys]/[Asp]	M w,app ^a /g mol^−1	Association number^b
				Catiomer	Aniomer
a Determined from Zimm plots of SLS data obtained at 1.0, 2.0, 3.0, 4.0 and 5.0 mg mL^−1. b Calculated from the mixing ratio and Mw,app shown in the third and the forth columns, respectively, and the averaged molecular weights of the examined polymers. c In ref. 11.
AB18	CH20	0.4	31 200	1.4	3.9
		0.6	33 900	2.2	4.0
		0.8	36 700	3.0	4.1
		1.0^c	3 430 000	212	235
AB18	CH82	0.4	78 400	1.1	10.2
		0.6	85 600	1.3	10.1
		0.8	91 300	1.8	10.2
		1.0^c	3 410 000	52	236
AB78	CH20	0.4	34 200	3.0	1.9
		0.6	42 100	4.9	2.1
		0.8	44 300	6.2	2.0
		1.0^c	7 470 000	1197	255
AB78	CH82	0.4	75 600	1.6	4.2
		0.6	82 300	2.3	4.1
		0.8	86 300	3.0	3.9
		1.0^c	7 510 000	289	304

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The determined M_w,app values for AB/CH complexes in non-stoichiometric conditions were two orders of magnitude lower than those for PIC micelles prepared in the stoichiometric condition. There was also a common trend for each combination that M_w,app values gradually increased with increasing [Lys]/[Asp], suggesting a change in the association number of the complex. Since homogeneous complexation should be confirmed to calculate the association number directly from M_w,app, analytical ultracentrifugation measurements were carried out on AB78/CH82 complexes to examine the distribution. Fig. 5 shows the sedimentation charts for AB78/CH82 at [Lys]/[Asp] = 0.4, 0.6 and 0.8. At all points of [Lys]/[Asp] evaluated here, unimodal peaks were detected. The peak position gradually shifted to higher sedimentation coefficients with an increase in [Lys]/[Asp]: the sedimentation coefficients at these peaks were 2.45, 2.85 and 3.25 svedbergs at [Lys]/[Asp] = 0.4, 0.6 and 0.8, respectively. This trend in peak shift is in line with the change in M_w,app summarized in Table 1. Accordingly, the association numbers of polyelectrolytes in AB/CH complexes can be calculated directly from the M_w,app summarized in Table 1 based on the residual molar ratio ([Lys]/[Asp]) and the molecular weight of each polyelectrolyte, assuming the homogeneous nature of the complexes. The calculated association numbers of CH and AB at varying [Lys]/[Asp] are also summarized in Table 1. Interestingly, the association number of AB was independent on [Lys]/[Asp], and was calculated to be 2, 4, 4 and 10 for AB78/CH20, AB78/CH82, AB18/CH20, and AB18/CH82, respectively. On the other hand, the association number of CH increased with an increase in [Lys]/[Asp]. This indicates that the increases in M_w,app (Table 1) and sedimentation coefficient (Fig. 5) with increasing [Lys]/[Asp] were mainly due to an increase in the association number of CH. That is, the associates of CH and AB in the region of [Lys] < [Asp] have characteristics similar to an inclusion complex (a host–guest complex), in which CH as guest polymer is included in the host associate composed of a definite number of AB strands. Interestingly, the complex had the same association number of 4 for anionic block-polyelectrolyte (AB), when the AB/CH pair had similar lengths of the charged segments, for example, AB18/CH20 and AB78/CH82. The shorter P(Asp) segment in AB than the P(Lys) segment of CH led to an increase in the association number of AB (AB18/CH82) to 10, and conversely, longer segments resulted in a decrease in the association number of AB (AB78/CH20) to 2. This trend is reasonable because more AB strands would be required to accommodate the longer CH in the complex.

Fig. 5 Distribution of the sedimentation coefficients for the PEG–P(Asp)/P(Lys) (AB78/CH82) system at [Lys]/[Asp] = 0.4, 0.6 and 0.8.

3.4. Molecular features of polyion complex formation from block- and homo-polyelectrolytes

As demonstrated in the preceding section, AB strands seem to behave as host molecules in the region of [Lys] < [Asp], where the anionic block-polyelectrolyte (AB) is a major component, and have an opportunity to participate in complexation with CH strands as guest molecules to form non-stoichiometric complexes with a definite association number, depending on the lengths of P(Asp) segments. Eventually, free AB strands are eliminated in the milieu. Alternatively, CH strands seem to always behave as guest molecules, even though they exist as the major component in the region of [Lys] > [Asp], and form stoichiometric PIC micelles with minor AB strands in a cooperative manner, as observed by DLS (Fig. 4), leaving excess CH strands in a free form in the milieu. This phenomenon may simply be described by assuming the increased association force of polyelectrolyte strands through the block copolymerization with PEG, and is consistent with the exclusive selection of the cationic block-polyelectrolyte (CB) by the anionic block-polyelectrolyte (AB) from the mixture of the cationic block- and homo-polyelectrolytes (CB and CH), as described in the preceding section (Fig. 1 and 2). It should also be noted that, as seen in Fig. 3 and 4, that pairs of oppositely charged block-polyelectrolytes with charged segments of matching lengths (AB78/CB78) follow a cooperative complexation scheme in all of the regions of residual molar ratio of charged units to form stoichiometric PIC micelles, suggesting that PEG conjugation to the minor charged components in the milieu may change the complexation manner from a loose non-cooperative association to a tight cooperative pairing, leading to growth into the stoichiometric core–shell PIC micelles with an appreciably high association number. The increased association force of block-polyelectrolytes compared with the corresponding homo-polyelectrolytes was directly demonstrated by measuring the chain exchange through GFC, as seen in Fig. 6. Here, AB78/CH82 micelles formed at stoichiometric ratios gave a single peak at the elution volume of 13.1 mL in the GFC chromatograph (chart (a) in Fig. 6). Addition of a stoichiometric amount of CB78 to the AB78/CH82 micelle solution to neutralize AB78, such that [Lys in CB78] = [Lys in CH82] = [Asp in AB78], led to the appearance of a new peak at 19.9 mL in GFC, corresponding to CH82 (see charts (b) and (c) in Fig. 6). This clearly indicates that the added CB78 selectively replaced CH82 in the original AB78/CH82 micelles to form AB78/CB78 micelles. Only a trace peak was observed at 17.1 mL, corresponding to the remaining free CB78 in the milieu, as shown in chart (b) of Fig. 6. Quantification of the relative peak areas for CB78 and CH82 in Fig. 6(b) allows us to calculate the exchange selectivity as 96%, which is consistent with the selectivity (95%) between cationic block- and homo-polyelectrolytes by anionic block-polyelectrolyte, as determined from Fig. 2. Furthermore, the result of Fig. 6 demonstrates that the association is able to shift to the thermodynamically favorable state through the polymer-exchange reaction, even after the formation of PIC micelles; thus, the system is in the condition of dynamic equilibrium.

Fig. 6 Release of P(Lys) (CH82) from PEG–P(Asp)/P(Lys) (AB78/CH82) micelles by the addition of PEG–P(Lys) (CB78). (a) GFC chart of PIC micelles from PEG–P(Asp) (AB78) and P(Lys) (CH82). (b) GFC chart after the addition of PEG–P(Lys) (CB78) toAB78/CH82 micelles. (c) GFC chart of CH82. (d) GFC chart of CB78.

4. Conclusion

This study revealed a new form of molecular recognition based on a difference in polymer architecture: a pair of oppositely charged block-polyelectrolytes principally select each other in a mixed aqueous solution of block- and homo-polyelectrolytes, excluding homo-polyelectrolytes from the formation of multi-molecular associates, PIC micelles. This phenomenon is unprecedented from the restricted conformation of block-polyelectrolytes in PIC micelles, i.e. the junction of PEG and polyelectrolytes segments in the block-polyelectrolytes to be aligned at the core–shell interface, as well as the increased PEG density in the shell compared to the micelle from a pair of block- and homo-polyelectrolytes, providing the same association number. There should be an inherent increase in the association force of block-polyelectrolytes to form PICs, compensating for these restrictions. An assumed increase in the association force of block-polyelectrolytes is also supported by the formation of non-stoichiometric PIC associates in the range where the block-polyelectrolytes is a major component.

The mechanisms involved in the increased association force of polyelectrolytes by PEG conjugation have not yet been fully elucidated. The formation of polyion complexes is well documented to be an entropy-driven process, and the major increase in entropy with polyion complexation is due to the release of counter ions from polyelectrolytes, which may compensate with an entropy loss due to a decrease in polymer mobility through complexation.²⁰ The amount of counter ions released with the complexation depends only on charge ratios of the polyelectrolyte pair, and may not be influenced by PEG conjugation. There is a decrease in the translational entropy of polyelectrolytes through PEG conjugation due to an increase in the molecular weight, which may become a factor increasing the association force of polymer strands. Furthermore, conjugation of incompatible segments, in this case PEG and P(Asp) or P(Lys), may reduce the conformational entropy of both strands in the solution due to long-range interactions, leading to the facilitated phase separation driven by polyion complexation to dispel this molecular frustration.²¹ All of these mechanisms remain in the hypothesis stage, and further detailed studies are necessary to clarify the unique molecular recognition discovered here. From a practical viewpoint, this new mode of molecular recognition based on polymer architecture may be integrated into various molecular systems to allow the design of dynamic functions responding to external stimuli.

Acknowledgements

The authors thank Dr James R. Christie II, The University of Tokyo, for editing the English of the manuscript. This work was partly supported by a Grant-in-Aid for Scientific Research from The Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan.

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Footnote

† Present address: Department of Applied Chemistry, Graduate School of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 591-8531, Japan.

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