Hydrodynamic Behavior of High Molar Mass Linear Polyglycidol in

The tacticity differs only very little upon the molar mass. For the ...... (c) Akcasu, A. Z.; Hammouda, B.; Lodge, T. P.; Han, C. C. Macromolecules 19...
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J. Phys. Chem. B 2007, 111, 11127-11133

11127

Hydrodynamic Behavior of High Molar Mass Linear Polyglycidol in Dilute Aqueous Solution S. Rangelov,*,† B. Trzebicka,‡ M. Jamroz-Piegza,‡ and A. Dworak‡,§ Institute of Polymers, Bulgarian Academy of Sciences, Acad. G. BoncheV 103-A, 1113 Sofia, Bulgaria, Centre of Polymer and Carbon Materials, Polish Academy of Sciences, M. Curie-Skłodowskiej 34, 41-819 Zabrze, Poland, and Institute of Chemistry, UniVersity of Opole, Oleska 48, 45-052 Opole, Poland ReceiVed: June 10, 2007; In Final Form: July 10, 2007

Six high molar mass polyglycidol samples were obtained by fractionation of polyglycidol synthesized by means of cationic polymerization of ethoxyethyl glycidyl ether followed by cleavage of the protective groups. The fractions covering the molar mass range from 0.1 to 2.4 × 106 were studied by dynamic and static light scattering. The weight-average molar masses (Mw), second virial coefficients (A2), radii of gyration (Rg), diffusion coefficients (D0), hydrodynamic radii (Rh), and dynamic virial coefficients (kDφ) were determined for the single coil in dilute aqueous solution at 25 °C, and scaling equations were established. It was found that polyglycidol in water does not exhibit the expected asymptotic good solvent behavior. The scaling exponents for A2, D0, and Rh are even closer to those for polymer coils in marginal solvents than to the expected ones in the excluded-volume region. The values of the interpenetration parameter, ψ, and kDφ are far from reaching limiting values even for the fractions of the highest molar masses. The scaling exponent for Rg as well as the Rg/Rh ratio, which was found to increase with increasing molar mass, imply elongated coil conformation in the high molar mass region.

Introduction Much of the literature on single-chain behavior in a thermodynamically good solvent is concerned with materials such as polydienes,1 polystyrene,2-4 poly(ethylene oxide),5,6 poly(Rmethylstyrene),7-9 poly(methyl methacrylate),10 polyacrylamide,11 and some biopolymers.12 Dynamic and static light scattering have been mainly used to investigate the interactions in both dilute and concentrated solution, to assess the light scattering parameters and derive scaling equations. The latter are of the power-law type (eq 1)

P ) CMν

(1)

where P is a given (light scattering) parameter, M is the chain molar mass, and C is a system-specific prefactor. As far as chain dimensions are concerned the scaling exponent, ν, increases from somewhat greater than 0.5 to =0.6 with increasing chain molar mass. The chain dimension here is either the chain hydrodynamic radius, Rh, or its radius of gyration, Rg. The above dependence is observed as a consequence of chain swelling due to the gradual increase in the effect of intrachain excluded volume;13a the Flory prediction for ν is 3/5 () 0.6) when the excluded-volume region is reached,13a whereas scaling theories expect 0.588.13b-g The scaling exponent for the second virial coefficient, A2, attains a value of -1/5 in good solvent conditions.13 As noted above, the prefactor C is system-specific and the scaling exponent is somewhat molar mass dependent since the location of the excluded-volume region is also systemspecific. For example, for the readily accessible molar mass * Corresponding author. Tel.: + 359 2 9792293. Fax: + 359 2 8700309. E-mail: [email protected]. † Bulgarian Academy of Sciences. ‡ Polish Academy of Sciences. § University of Opole.

Figure 1. Chemical structures of the monomer units of (a) poly(ethylene oxide) and (b) linear polyglycidol.

range of 105 to 106, poly(ethylene oxide) (PEO) in water exhibits asymptotic good solvent behavior,5a whereas the buildup of the excluded-volume effect can be so gradual so that the theoretical values for the scaling exponents of other systems can be reached at considerably higher (tens of millions) molar masses.4a Table 1 summarizes literature data for the values of C and ν for various polymer-good solvent systems. Particularly for the PEO-water systems it can be noted that the actual values of A2, Rg, and Rh are much larger than those for other linear flexible polymers in good solvents, which is reflected by the larger prefactors in the scaling relations (Table 1). These data indicate that water is an extremely good solvent for PEO, which has been attributed to the unusual ability of water molecules to pack into and swell PEO coils.5a PEO is sterically thin (see Figure 1 for the structural formula of the monomer unit), flexible, and offers similar ether oxygen spacing (2.88 Å) to that of the oxygen in water (2.85 Å), which provides an excellent fit of the PEO coil to the structure of water. Interestingly, in the crystalline state PEO adopts a helical conformation,14 which, as hypothesized earlier,15 is partially retained even in dilute aqueous solution. Recently, the attention of a number of scientific teams has been attracted by another member of the polyepoxides, polyg-

10.1021/jp074485q CCC: $37.00 © 2007 American Chemical Society Published on Web 09/06/2007

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Rangelov et al.

TABLE 1: Values of the Prefactor C and the Scaling Exponent ν in P ) CMν for Selected Systemsa C

ν

9 × 10-3 0.0116 0.0149 5.24 × 10-4 0.00749

-0.28 0.566 0.58 -0.59 0.59 -0.28 -0.29

7b 7b, Rh in nm 7c, Rg in nm 7c, D0 in cm2‚s-1 7c, Rh in nm 7c 7a

0.0137 0.0136 8.34 × 10-3

0.595 0.573 -0.213

1, Rg in nm 1, Rh in nm 1

0.0215 1.84 × 10-2 0.0145

0.583 -0.20 0.571 0.59 0.39 -0.57

5b, Rg in nm 5b 5b, Rh in nm 6b 6b, microgel formation 5c

polybutadiene/cyclohexane Rg (0.1 × 105 < M < 7.6 × 105) Rh (0.1 × 105 < M < 7.6 × 105) A2 (0.1 × 105 < M < 7.6 × 105)

0.0129 0.015 1.23 × 10-3

0.609 0.570 -0.212

1, Rg in nm 1, Rh in nm 1

polyisoprene/cyclohexane Rg (0.15 × 105 < M < 72.4 × 105) Rh (0.15 × 105 < M < 72.4 × 105) A2 (0.15 × 105 < M < 72.4 × 105)

0.0126 0.0113 0.0132

0.610 0.592 -0.232

1, Rg in nm 1, Rh in nm 1

polystyrene/toluene D0 (M > 30 000) A2 (M > 105) Rg (M > 105)

3.40 × 10-4 4.36 × 10-3 0.0125

-0.578 -0.203 0.595

2a, D0 in cm2‚s-1 2a 2a, Rg in nm

-0.665 0.64 0.67

12a 12a 12b

system poly(R-methylstyrene)/toluene A2 (M > 50 000) Rh (M > 50 000) Rg (5 × 103 < M < 106) D0 (5 × 103 < M < 106) Rh (5 × 103 < M < 106) A2 (5 × 103 < M < 106) A2 polyisobutylene/cyclohexane Rg (1.6 × 105 < M < 1.41 × 107) Rh (1.6 × 105 < M < 1.41 × 107) A2 (1.6 × 105 < M < 1.41 × 107) poly(ethylene oxide)/water Rg (86 000 < M < 996 000) A2 (86 000 < M < 996 000) Rh (86 000 < M < 996 000) Rh (M > 106) Rg (M > 106) D0 (3400 < M < 4 × 106)

chitosan/aqueous solution D0 Rg Rh and Rg a

refs and notes

Here P is a given light scattering parameter, and M is chain molar mass.

TABLE 2: Molar Mass of Polyglycidol Fractions from SEC-MALLS Measurements no.

fraction

10-6 × Mn (Da)

1 2 3 4 5 6

PG1 PG2 PG3 PG4 PG5 PG6

2.10 1.70 0.616 0.453 0.118 0.088

10-6 × Mw (Da)

Mw/Mn

2.43 2.28 1.16 0.552 0.187 0.110

1.20 1.43 1.80 1.22 1.58 1.25

lycidol (PG). The linear analogue is structurally similar to PEO; however, it bears a hydroxyl group in each monomeric unit (Figure 1). This makes it an interesting precursor of hydrophobic and amphiphilic polymeric materials, especially since the ways of obtaining such polymers of controlled structure have been opened.16 In comparison to PEO, PG is considerably less studied. With this paper we aim to increase the knowledge on this interesting polymer by elucidating its aqueous solution properties in dilute limit. The resulting knowledge would be helpful for better understanding the behavior of PG in intermolecular interactions, interactions with (biological) surfaces, chemical and enzymatic reactions in aqueous solution, etc. In particular, by using a light scattering technique we aim to determine the static and dynamic parameters and the actual values of C and ν. The behavior of six well-defined samples of linear PG in water at 25 °C was studied by static and dynamic light scattering. The samples cover the molar mass range from 0.1 to 2.4 × 106.

Experimental Section Materials. Ethoxyethyl glycidyl ether (EEGE) was obtained by reacting 2,3-epoxypropanol-1 (glycidol) with ethyl vinyl ether according to procedure described by Fitton et al.17 The obtained product was fractionated under reduced pressure. Fraction of purity exceeding 99.8% (GC) was used for polymerization. Diethyl ether was refluxed over Na/K alloy. Diethyl zinc (1 M solution in hexane, Aldrich) was used as received. Acetone was distilled before use. Polymerization of Ethoxyethyl Glycidyl Ether. EEGE was polymerized in bulk with ZnEt2/H2O (1:0.78) as catalyst using a similar procedure as described by Haouet et al.18 A 1 M solution of diethyl zinc in hexane (25 mL) was added into diethyl ether (25 mL) cooled to -10 °C. Deionized water (0.019 mol, 0.352 mL) was slowly dropped during 6 h into this solution (1 droplet/2 min). The mixture was stirred for 24 h at room temperature. Next, the solvents were evaporated and the EEGE (0.25 mol, 35 mL) was introduced. The molar ratio of diethyl zinc to monomer was 1:10. The polymerization was carried out for 24 h at 56 °C. The resulting poly(ethoxyethyl glycidyl ether) was hydrolyzed using 3 M HCl. The polymer solution was filtered and desalinated by dialysis against water. Water was evaporated, and the obtained PG was dried under reduced pressure. Fractionation. An amount of 1.7 g of PG was dissolved in 280 mL of deionized water (polymer concentration in solution was 6 g/L). The solution was intensively stirred, and acetone

Hydrodynamic Behavior of Linear Polyglycidol

Figure 2.

13

J. Phys. Chem. B, Vol. 111, No. 38, 2007 11129

C NMR spectrum of PG2.

Figure 3. Relaxation time distributions measured at angle 90° and temperature 25 °C for a 2.0 mg‚mL-1 solution of PG4 (a) and a 0.96 mg‚mL-1 solution of PG2 (b).

was slowly added under stirring. When the first opacity was observed, an additional 2 mL of acetone was added. The suspension was centrifuged. The solution was decanted from the precipitated polymer and subjected again to the fractionation procedure. The polymer fractions were dried under reduced pressure at 30 °C. This procedure was repeated until no more opacity was observed when adding acetone. Methods. Nuclear Magnetic Resonance (NMR). The 1H and 13C NMR spectra of PG were recorded in D O using a Bruker 2 Avance Ultra Shield spectrometer operating at 400 MHz. Size Exclusion Chromatography (SEC). The molar masses and dispersities of the obtained PG and its fractions were determined by SEC using a multiangle light scattering detector (λ ) 658 nm) DAWN HELEOS of Wyatt Technology and a refractive index detector ∆n-1000 RI from WGE DR Bures. SEC measurements were performed at 45 °C in DMF with 5 mmol/L LiBr at a nominal flow rate of 1 mL/min. Three columns PSS GRAM, 30 Å, 102 Å, and 103 Å, (Polymer Standards Services) were used. Results were evaluated using the ASTRA 4.73 software from Wyatt Technologies and

WINGPC 6.0 software from PSS. The refractive index increment (dn/dc) of PG in DMF was measured independently to 0.054 mL/g. Dynamic Light Scattering (DLS). DLS measurements were performed on a Brookhaven BI-200 goniometer with vertically polarized incident light of wavelength λ ) 632.8 nm supplied by a He-Ne laser operating at 75 mW and a Brookhaven BI9000 AT digital autocorrelator. Measurements of the scattered light from the polymer aqueous solutions were made at angles θ ranging from 40° to 140°. The autocorrelation functions were analyzed using the constrained regularized algorithm CONTIN19 to obtain distributions of relaxation times (τ). The probabilityto-reject parameter was fixed at 0.5. The relaxation rates, Γ () τ-1), give distributions of the apparent diffusion coefficients (D ) Γ/q2). Here, q is the magnitude of the scattering vector given by q ) (4πn/λ) sin(θ/2) and n is the refractive index of the medium. The mean hydrodynamic radius is obtained by the equation of Stokes-Einstein:

Rh ) kT/(6πηD0)

(2)

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Rangelov et al.

Figure 4. Relaxation rate (Γ) as a function of sin2(θ/2) for the fast and dominant modes observed for a 0.48 mg‚mL-1 solution of PG2 (closed squares in (a) and (b), respectively) and for a 2.203 mg‚mL-1 solution of PG6 (open squares in (b)). The lines through the data points in (b) represent the linear fits to the data.

where k is the Boltzmann constant, η is the solvent viscosity at temperature T in K, and D0 is the diffusion coefficient at infinite dilution. Static Light Scattering (SLS). SLS measurements were carried out using the same light scattering set and the same angle interval. The SLS data were analyzed using the Zimm plot software (BI-ZPW) provided by Brookhaven Instruments. Information on the weight-average molar mass, Mw, the radius of gyration, and the second virial coefficient was obtained from the dependence of the quantity Kc/Rθ on the concentration, c, and scattering angle, θ. Here the optical constant K is defined by

K ) 4π2n02(dn/dc)2/NAλ4

(3)

where n0 is the refractive index of water, NA is Avogadro’s constant, λ is the laser wavelength, and dn/dc is the refractive index increment, measured using differential refractive index detector ∆n-1000 RI WGE DR Bures. Rθ is the Rayleigh ratio of the polymer solution at θ. Results Sample Preparation and Characterization. The molar masses and dispersities of parent PG and the samples obtained as a result of its fractionation were measured by size exclusion chromatography multiangle laser light scattering (SECMALLS). For the parent PG Mn ) 1.054 × 106, Mw ) 1.7 × 106, and a dispersity of 1.8 were obtained. The SEC trace (not shown) of this polymer was broad but monomodal. The molar masses and dispersities of the fractions are collected in Table 2. Tacticity. The Vandenberg coordinative catalysts based upon diethyl zinc are known to lead to at least partially isotactic polymers when applied to the polymerization of asymmetric oxiranes.18 When the polymers resulting from such processes are fractionated, the fractionation may occur according to the molar mass and the tacticity, as the isotactic polymers are less soluble then the atactic ones. As the aim of this work is to study how the hydrodynamic parameters change with the molar mass, it was necessary to make sure that the molar mass is the only criterion for the fractionation. Should the tacticity of the fractionated samples also vary, the results would be blurred and their analysis difficult. 13C NMR was used to determine the tacticity of the fractionated samples. The peaks of the methylene group are

clearly split into signals of the dyads and those of the hydroxymethyl side group into the signals of triads, as shown in Figure 2. The tacticity differs only very little upon the molar mass. For the low molar mass fraction (entry 6 in Table 2) the content of the isotactic dyads is 69%, for the highest molar mass (entry 1 in Table 2) fraction it is 72%. The results for the other fractions are between these two values. The difference is very small and is not likely to influence the hydrodynamic data. Signals of triads are also well separated in the spectra, which permits us to determine whether the chains are Bernoullian. They are clearly of non-Bernoullian character. The first-order Markov conditional probabilities are Pm/r ) 0.22-0.19, Pr/m ) 0.50-0.47. Light Scattering Study. DLS. The aqueous solution behavior of the six fractions obtained from the parent PG was investigated in the dilute regime. Figure 3 shows relaxation time distributions obtained from representative fractions of the higher and lower molar masses. Whereas the distribution for sample PG4 (a representative of the lower molar mass fractions) is clearly monomodal (Figure 3a), that of PG2 (a representative of the higher molar mass fractions) contains a fast mode of amplitude accounted at angle 90° of about 2% (Figure 3b). For PG3, PG4, and PG5 the qRg values were in the interval of 0.15-1.35 and bimodal distributions were only occasionally observed. The frequency of the appearance of bimodal distributions reached 60% for the high molar mass fractions (PG1 and PG2). It has been shown elsewhere20a that when qRg > 1 the motion observed in DLS might be nondiffusive. This is clearly evident from the angular dependence of the relaxation rate, Γ, of the fast mode4c,6b,20b,c depicted in Figure 4a. Consequently, the fast modes most probably derive from internal motions of the large PG chains and are of marginal interest as far as determination of the light scattering parameters such as molar masses are concerned. The slower peaks of the bimodal distributions are shown to be diffusive as exemplified in Figure 4b for PG2. So are the peaks of the monomodal distributions, exhibited by the lower molar mass fractions (Figure 4b). The diffusion coefficients were determined from the slopes of the linear plots of Γ versus sin2(θ/2) and then plotted against concentration and extrapolated to zero concentration (Figure 5). D0 values were taken as intercept values from these plots, and Rh values were evaluated using eq 2. Another parameter that can be extracted from the DLS data is the dynamic virial coefficient, kDc, obtained from the virial expansion of the concentration dependence of diffusion coef-

Hydrodynamic Behavior of Linear Polyglycidol

J. Phys. Chem. B, Vol. 111, No. 38, 2007 11131 TABLE 3: Dynamic Light Scattering Characterization Data fraction PG1 PG2 PG3 PG4 PG5 PG6

1012 × D0 (m2‚s-1)

Rh (nm)

kDc (mL‚g-1)

kDφ

6.617 6.794 9.244 14.786 24.913 32.937

37.0 36.1 26.5 16.6 9.8 7.4

28.56 -0.31 -1.15 -1.89 -1.96 -2.13

0.52 -0.005 -0.03 -0.072 -0.16 -0.21

TABLE 4: Static Light Scattering Characterization Data fraction Figure 5. Concentration dependence for the diffusion coefficients for PG1 (closed triangles), PG2 (open triangles), PG3 (diamonds), PG4 (inverted triangles), PG5 (circles), and PG6 (squares).

PG1 PG2 PG3 PG4 PG5 PG6

10-6 × Mw (g‚mol-1)

Rg (nm)

104 × A2 (mL‚mol‚g-2)

2.330 1.806 1.093 0.446 0.199 0.103

85.3 82.2 54.6 28.2 16.1

4.40 4.31 4.74 5.35 6.15 5.59

Rg/Rh

ψ

2.27 2.33 2.04 1.43 1.68

0.347 0.228 0.314 0.428 0.527

the ratio Rg/Rh, which is given in Table 4. Another measure of the aqueous solution behavior of PG is the interpenetration function, ψ. It is a dimensionless parameter, defined by eq 6, that is used to assess the extent of interpenetration of polymer chains in dilute solution. The values of ψ are presented in the last column of Table 4.

ψ ) A2M2/4π3/2NARg3

(6)

Discussion Figure 6. Zimm plot of PG1 in water at 25 °C: experimental points (open symbols); extrapolated points (closed symbols).

ficient (eq 4). Experimentally, kDc was obtained from the slopes of the D versus concentration plots in Figure 5.

D ) D0 (1 + kDcc)

(4)

This virial coefficient provides useful information about chainchain hydrodynamic interactions in dilute solution. The positive values indicate a swollen state of the macromolecules, that is, the existence of repulsive interactions between the chain units. The theoretical predictions typically treat the dynamic virial coefficient in volume fraction units, kDφ. The conversion between the weight and volume fraction parameters is given by eq 5.13e

kDφ ) (M/NAVh)kDc

(5)

where Vh is the hydrodynamic volume, obtained using Rh, and M is the molar mass. The values of molar masses from SLS (see the next section) were used to calculate kDφ. All DLS parameters are collected in Table 3. SLS. Zimm plot analyses of SLS measurements provided Mw, A2, and Rg values. A typical Zimm plot is shown in Figure 6 for PG1. For all fractions Kc/Rθ were linearly dependent on sin2(θ/2). The static parameters are summarized in Table 4. The values of Mw obtained from SLS are in reasonable agreement with the values from SEC-MALLS (Tables 2 and 4); the differences between the Mw values from SLS and SECMALLS were typically below 6% being somewhat larger (ca. 20%) for PG2 and PG4. The second virial coefficients were invariably positive, indicating favorable polymer/solvent interactions. The combination of dynamic and static parameters yields

The double-logarithmic molar mass dependences of the static (A2 and Rg) and dynamic (D0 and Rh) parameters are presented in Figure 7. The data arrange on straight lines with correlation factors typically above 0.99. This means that neglecting a certain point hardly influences the values of the prefactors and exponents in the scaling equations. Also, due to the reasonable agreement between the values of the molar masses obtained from SEC-MALLS and SLS the variations in the above parameters upon the substitution of the molar mass data from SLS with those from SEC-MALLS are within the statistical uncertainty. The results in the following are presented as a function of Mw from SLS. The results for A2 are presented in Figure 7a. As clearly seen from the figure, A2 values exhibit in the low molar mass region a downward deviation from the straight line. Interestingly, some theories21 predict exactly a downward curvature at low Mw, which has not been experimentally observed for flexible chains in good solvents.2,3a,7b For Mw > 105 the following relation was found:

A2 ) (3.57 × 10-3)Mw-0.145

(in mL‚mol‚g-2)

It should be noted that the values of A2 are an order of magnitude lower than those of PEO in water5a,6b and comparable to those for polystyrene or poly(R-methylstyrene) in toluene.2a,7b,c What is different is the less pronounced molar mass dependence, reflected by the scaling exponent. Whereas an exponent of -0.2 is expected in good solvent conditions, a more pronounced molar mass dependence is predicted22 with decreasing solvent quality reaching -0.5 in poor solvents. However, to the best of our knowledge, such a pronounced molar mass dependence has not been observed: negligible dependence or even independency of molar mass have been reported for polystyrene in cyclohexane and polyisoprene in dioxane at temperatures below Θ temperature, respectively.2b,7b,23 In that context, this finding may

11132 J. Phys. Chem. B, Vol. 111, No. 38, 2007

Rangelov et al. why the scaling relation for Rg was derived for Mw g 2 × 105. The molar mass dependence of Rg is depicted in Figure 7c. It is immediately seen that the lines for Rg and Rh are somewhat diverging, which is quantified by the difference in the scaling exponents for Rh and Rg. For the radius of gyration the following scaling relation was obtained:

Rg ) (2.972 × 10-3)Mw0.705

Figure 7. Molar mass dependences of the second virial coefficient (a), diffusion coefficient (b), and radius of gyration (circles) and hydrodynamic radius (triangles) in (c) for high molar mass linear polyglycidol samples in water at 25 °C. The lines through the data points represent the linear fits to the data.

indicate that water is a worse solvent for PG than, for example, it is for PEO or toluene is for polystyrene or poly(R-methylstyrene). Log-log plots of D0 and Rh versus Mw are presented in Figure 7, parts b and c, respectively. The linear fits yielded

D0 ) (1.72 × 10-8)Mw-0.542

(in m2‚s-1)

and, correspondingly,

Rh ) 0.0139Mw0.542

(in nm)

Here, we observe again small but noticeable deviations in the scaling exponents. The latter are lower than the Flory prediction and seem closer to the exponents observed in marginal solvents, that is, 0.514.7b It was not possible to define the radius of gyration for the fraction PG6 due to the small molecular dimensions. That is

(in nm)

As seen from the equation the scaling exponent for Rg is higher than that for Rh. Such a divergence is to be expected in regions where the asymptotic behavior is not reached since, as noted elsewhere,13d Rg reaches its asymptotic value faster than Rh. The two scaling exponents are markedly different, which implies that a variation of the Rg/Rh ratio (Table 4) with molar mass is observed. The Rg/Rh ratio decreases with decreasing molar mass from a relatively high value of 2.3 to about 1.4 at Mw = 105 implying that the PG coils are more compact at lower molar masses. However, what is even more peculiar is that the exponent is higher than the theoretically predicted one. This could be attributed to the dispersity of the fractions. In samples of high dispersity Rg and, consequently the Rg/Rh ratio, is overestimated. We can expect that the scaling exponent for Rg is overestimated as well. Furthermore, as seen from Table 2, the dispersity does not change systematically with molar mass, which could result in scattering in the Rg values and possibly contribute to the overestimation of Rg and the parameters derived from Rg. It is noteworthy that a relatively high (0.67) scaling exponent for Rg has been observed for chitosans in aqueous solution.12b The authors produce evidence for a nearly freedraining flexible wormlike chain typified by a persistence length of several nanometers, whose hydrodynamically equivalent body is a prolate ellipsoid. Considering the chemical structure of the PG units (Figure 1) we may speculate on the existence of steric/ rotational hindrance in the PG macromolecules resulting in chain stiffness and formation of (slightly) elongated coils. Such a structure could be stabilized by intramolecular H-bonding between the hydroxyl groups mediated by water molecules. No doubt, further experiments are needed to confirm this speculation. Next, the behavior of the dynamic virial coefficient, kD, is considered (Table 3). Typically, kD values depend on Mw: whereas in Θ solvents kD is negative and decreases with increasing molar mass,2a,24 in good solvents or above the Θ temperature kD is mostly positive and increases with increasing molar mass. In particular, kDφ tends to attain a limiting value at sufficiently high molar mass. For polystyrene in toluene or benzene a limiting value of 2.7 at molar mass of about 106 was observed,7c whereas kDφ values (≈2) for PEO in water show independence on molar mass at considerably lower molar masses (2 × 105 to 1 × 106 g‚mol-1).5a The limiting kDφ values for both polystyrene/toluene (or benzene) and PEO/water are consistent with the theoretical predictions.8a,25 It is evident from Table 3 that the kDφ values of the present system are molar mass dependent, however, far from reaching a limiting value. The values of the diffusion virial coefficients are comparable in magnitude to those of polystyrene in cyclohexane at 50 °C, which is slightly above the Θ temperature (35 °C).7b The interpenetration function ψ has been found to increase toward lower molar mass, whereas in the excluded-volume region it is constant. The predicted asymptotic values at large Mw limit in good solvents are within the range of 0.23-0.27.26 The results from the explicit calculations of ψ for each fraction are presented in the last column of Table 4. The interpenetration function is not constant exhibiting moderate Mw dependence.

Hydrodynamic Behavior of Linear Polyglycidol Conclusions The behavior of high molar mass PG in dilute aqueous solution is complex and far from unambiguous. Considering the widely accepted view of the extremely highly hydrophilic polymer we anticipated well-expanded coils, exhibiting good solvent behavior in water and scaling exponents having reached values predicted by the theory. In addition, the introduction of hydroxymethylene groups was expected to have shifted the crossover between the Gaussian and excluded-volume regions downward, that is, toward lower molar masses. Instead, the molar mass dependences of A2, D0, Rh, kDφ, and ψ did not exhibit asymptotic good solvent behavior in water at 25 °C and in the investigated molar mass range indicating that PG has not completed the transition into the excluded-volume region. What is even more surprising is that the numerical values of kDφ and the scaling exponents for A2 and D0 (Rh, respectively) are closer to those observed for linear chains in a marginal solvent, e.g., polystyrene in cyclohexane at 50 °C, than to those in a good solvent. In particular, the kDφ values were found to increase with increasing molar mass but are mostly negative and close to zero thus being comparable to those for polystyrene in cyclohexane at 50 °C. The less pronounced molar mass dependences of A2 (scaling exponent of -0.145) and D0 or Rh (-0.542 or 0.542, respectively) may indicate that water at 25 °C provides for PG markedly worse solvent conditions than for its structural analogue PEO. A deviation from the established power law was observed for Rg. Further experiments are in progress to prove that, as suggested here, PG tends to adopt elongated coil conformation that is detectable in the high molar mass limit. Acknowledgment. This work was supported by the European Commission Project NANOSTIM No. MTKD-CT-2004509841. M.J.-P. appreciates the fellowship granted by the Regional Found of the Ph.D. Scholarships. References and Notes (1) Fetters, L. J.; Hadjichristidis, N.; Lindner, J. S.; Mays, J. W. J. Phys. Chem. Ref. Data 1994, 23, 619-640. (2) (a) Huber, K.; Bantle, S.; Lutz, P.; Burchard, W. Macromolecules 1985, 18, 1461-1467. (b) Fujita, H. Macromolecules 1988, 21, 179. (c) Fujita, H.; Norisuye, T. Macromolecules 1985, 18, 1637. (3) (a) Miyaki, Y.; Einaga, Y.; Fujita, H. Macromolecules 1978, 11, 1180. (b) Akcasu, A. Z.; Han, C. C. Macromolecules 1979, 12, 276. (c) Adam, M.; Delsanti, M. J. Phys. (Paris) 1976, 37, 1045. (d) Schaefer, D. W.; Joanny, J. F.; Pincus, P. Macromolecules 1980, 13, 1280. (4) (a) Appelt, B.; Meyerhoff, G. Macromolecules 1980, 13, 657. (b) Bantle, S.; Schmidt, M.; Burchard, W. Macromolecules 1982, 15, 1604. (c) Nicolai, T.; Brown, W.; Johnsen, R. Macromolecules 1989, 22, 27952801. (5) (a) Devanand, K.; Selser, J. C. Macromolecules 1991, 24, 59435947. (b) Woodley, D. M.; Dam, C.; Lam, H.; LeCave, M.; Devanand, K.; Selser, J. Macromolecules 1992, 25, 5283-5286. (c) Branca, C.; Faraone,

J. Phys. Chem. B, Vol. 111, No. 38, 2007 11133 A.; Magazu, S.; Maisano, G.; Migliardo, P.; Villari, V. J. Mol. Liq. 2000, 87, 21-68. (6) (a) Brown, W.; Stilbs, P.; Johnsen, R. M. J. Polym. Sci., Polym. Phys. Ed. 1983, 21, 1029. (b) Rangelov, S.; Brown, W. Polymer 2000, 41, 4825-4830. (7) (a) Kato, T.; Miyaso, K.; Noda, I.; Fujimoto, T.; Nagasawa, M. Macromolecules 1970, 3, 777. (b) Cotts, P. M.; Selser, J. C. Macromolecules 1990, 23, 2050-2057. (c) Selser, J. C. Macromolecules 1981, 14, 346351. (8) (a) Akcasu, A. Z.; Benmouna, M. Macromolecules 1978, 11, 1193. (b) Akcasu, A. Z. Polymer 1981, 22, 1169. (c) Akcasu, A. Z.; Hammouda, B.; Lodge, T. P.; Han, C. C. Macromolecules 1984, 17, 759. (9) (a) Han, C. C.; Akcasu, A. Z. Polymer 1981, 22, 1165. (b) van den Berg, H.; Jamieson, A. M. J. Polym. Sci., Polym. Phys. Ed. 1983, 21, 2311. (c) Huber, K.; Burchard, W.; Akcasu, A. Z. Macromolecules 1985, 18, 2743. (10) ter Meer, H.-U.; Burchard, W.; Wunderlich, W. Colloid Polym. Sci. 1980, 285, 675. (11) Patterson, P. M.; Jamieson, A. M. Macromolecules 1983, 18, 266. (12) (a) Wu, C.; Zhou, S.; Wang, W. Biopolymers 1995, 35, 385-392. (b) Colfen, H.; Berth, G.; Dautzenberg, H. Carbohydr. Polym. 2001, 45, 373-383. (13) (a) Flory, P. J. Principles of Polymer Chemistry; Cornell University Press: Ithaca, NY, 1953; Chapter XIV. (b) de Gennes, P. G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, 1979. (c) Le Guillou, J. C.; Zinn-Justin, J. J. Phys. ReV. Lett. 1977, 39, 95. (d) Weill, G.; des Cloizeaux, J. J. J. Phys. (Paris) 1979, 40, 99. (e) Yamakawa, H. Modern Theory of Polymer Solutions; Harper and Row: New York, 1971. (f) Fujita, H. Polymer Solutions; Elsevier: Amsterdam, 1990. (g) Des Cloizeaux, J.; Jannink, G. Polymers in Solution; Clarendon Press: Oxford, 1990. (14) (a) Rabolt, J. F.; Johnson, K. W.; Zitter, R. N. J. Chem. Phys. 1974, 61, 504. (b) Koenig, J. L.; Angood, A. C. J. Polym. Sci. 1970, 23, 1787. (c) Miyazawa, T. J. Chem. Phys. 1961, 35, 693. (15) Matsura, H.; Fukuhara, K. J. Mol. Struct. 1985, 126, 251. (16) (a) Taton, D.; LeBorgne, A.; Sepulchre, M.; Spassky, N. Macromol. Chem. Phys. 1994, 195, 139. (b) Jamro´z-Piegza, M.; Utrata-Wesolek, A.; Trzebicka, B.; Dworak, A. Eur. Polym. J. 2006, 42, 2497. (c) Dworak, A.; Panchev, I.; Trzebicka, B.; Wałach, W. Macromol. Symp. 2000, 153, 233. (d) Vandenberg, E. J. J. Macromol. Sci. Chem. 1985, A22, 619. (e) Halacheva, S.; Rangelov, S.; Tsvetanov, Ch. Macromolecules 2006, 39, 6845. (17) Fitton, A.; Hill, J.; Jane, D.; Miller, R. Synthesis 1987, 1140. (18) Haouet, A.; Sepulchre, M.; Spassky, N. Eur. Polym. J. 1983, 19 (12), 1089. (19) Provencher, S. W. Macromol. Chem. 1979, 180, 201. (20) (a) Doi, M.; Edwards, S. F. The Theory of Polymer Dynamics; Clarendon Press: Oxford, U.K., 1986. (b) Schillen, K.; Brown, W.; Johnsen, R. Macromolecules 1994, 27, 4825-4832. (c) Tsunashima, Y.; Nemoto, N.; Kurata, M. Macromolecules 1983, 16, 584. (21) Tanaka, G. J. Polym. Sci., Polym. Phys. Ed. 1979, 17, 305. (22) (a) Sanchez, I. C.; Lohse, D. J. Macromolecules 1981, 14, 131. (b) Rabin, Y. J. Chem. Phys. 1983, 79, 3988. (23) (a) Tong, Z.; Ohashi, S.; Einaga, Y.; Fujita, H. Polym. J. 1983, 11, 835. (b) Perzinski, R.; Delsanti, M.; Adam, M. J. Phys. 1987, 48, 115. (c) Takano, N.; Einaga, Y.; Fujita, H. Polym. J. 1985, 17, 1123. (24) (a) King, T. A.; Knox, A.; Lee, W. I.; McAdam, J. D. C. Polymer 1973, 14, 151. (b) Han, C. C.; McCrackin, F. L. Polymer 1979, 20, 427. (c) Jones, G.; Caroline, J. J. Chem. Phys. 1979, 37, 187. (25) (a) Yamakawa, H. J. Chem. Phys. 1962, 36, 2995. (b) Pyun, C. W.; Fixman, M. J. Chem. Phys. 1964, 41, 937. (26) (a) Oono, Y.; Freed, K. F. J. Phys. A: Math. Gen. 1982, 15, 1931. (b) Witten, T. A.; Schafer, L. J. Phys. A: Math. Gen. 1978, 11, 1843. (c) Stockmayer, W. H. Makromol. Chem. 1960, 35, 54.