DETERMINATION
Absolute techniques for MW determination include mem- brane osmometry, static light scattering and equilibrium sedimentation. These techniques require no assumptions about molecular conformation and do not require calibra- tion employing standards of known MW. Relative tech- niques include gel permeation chromatography (GPC), dynamic light scattering, velocity sedimentation and vis- cometry, and require either knowledge/assumptions con- cerning macromolecular conformation or calibration using standards of known MW. Combined techniques use infor- mation from two or more methods, such as velocity sedi- mentation combined with dynamic light scattering, velocity sedimentation combined with intrinsic viscosity measure- ments, and GPC combined with on-line (or off-line) static light scattering or equilibrium sedimentation.
1. Osmometry
Polymer solutions exert osmotic pressure across a porous boundary because the chemical potentials of a pure solvent and the solvent in a polymer solution are unequal. There is a thermodynamic drive toward dilution of the polymer-containing solution with a net flow of solvent through a separating membrane, toward the side contain- ing the polymer. When sufficient pressure is built up on the solution side of the membrane, equilibrium is restored. The osmotic pressure πdepends on Mnand polymer con- centration c as follows (58):
π⫽ RT
冢
⫹ A2c2⫹ A3c3⫹…冣
(2.5)where R is the molar universal gas constant, T is the absolute temperature, and A2and A3 are the second and the third virial coefficients, respectively. In very dilute solu- tions, it is usually sufficient to consider only the first two terms in the equation, which can then be rearranged as:
⫽ ⫹RTA2c (2.6)
where π/c is called the reduced osmotic pressure. According to the above equation, Mnmay be determined by a plot of π/c versus c extrapolated to zero concentration. The inter- cept gives RT/Mn, and the slope of the plot yields A2.
For neutral polysaccharides, osmotic pressure meas- urements can be made in water. However, for charged polysaccharides, salt solutions should be used to suppress the charge effects on apparent molecular weights. Usually 0.1–1 M NaCl or LiI is of sufficient ionic strength. Since osmotic pressure is dependent on the number of molecules present in solution, it is less sensitive to high MW poly- saccharides. In practice, this method is only useful for polysaccharides having MW less than 500,000 g/mol (59).
2. Static Light Scattering
Static light scattering is widely used for determining the MW of macromolecules and measures Mw. For a highly
dilute solution, the normalized intensity of scattered light R(q) as a function of scattering wave vector (q) and con- centration (c) is given as (60):
⫽ ⫹ 2A2c (2.7)
where K is a contrast constant and P(q) is the particle scat- tering factor. For a random coil, P(q) is expressed by:
P(q)⫽ 1 ⫺ ⫹… (2.8) and q⫽ sin
冢 冣
(2.9) where λis the wavelength,θis the scattering angle, and Rgis the radius of gyration. Equations 2.7–2.9 form theθ ᎏ2 4π ᎏλ q2R2 g ᎏ3 1 ᎏM wP(q) Kc ᎏR(q) RT ᎏM n π ᎏc c ᎏM n
冱
∞ i⫽1 Mi1⫹αN i ᎏᎏ冱
∞ i⫽1 MiNi冱
i⫽1∞M3 iNi ᎏ冱
∞ i⫽1 M2 iNi冱
∞ i⫽1 M2 iNi ᎏ冱
i⫽1∞MiNi冱
∞ i⫽1 MiNi ᎏ冱
i⫽1∞Nibasic theory for MW determination using static light scat- tering. In practice, this is done by measuring the angular dependence of scattered light from a series of dilute solu- tions. The scattering data are then processed in the form of a Zimm plot or other associated plots (Berry and Gunniur plots). In a typical Zimm plot, Kc/R(q, c) is plot- ted against q2 ⫹ kc, where k is an arbitrary constant to
separate the angle-dependent curves from different con- centrations. The double extrapolation to c⫽ 0 and q ⫽ 0 (i.e.,θ⫽0) results in two limiting curves intersecting the ordinate at the same point. This point gives 1/Mw. The ini-
tial slope of the curve at θ⫽ 0 is 2A2, and from the initial
slope of the curve at c⫽ 0, Rgis obtained. Figure 2.3 is a
Zimm plot of (1→3) (1→4)-β-D-glucan tricarbanilate measured in dioxan by static light scattering.
The measurement of the MW of polysaccharides by light scattering has not been an easy task when compared to many other macromolecules. The major difficulty is the preparation of optically clear solutions that are free of dust and molecular aggregates. A detailed procedure for the preparation and clarification of polymer solutions is given by Tabor (61) and Harding et al. (59). The meas- urement of MW is especially complicated by the exis- tence of aggregates. Extreme caution has to be taken in interpreting the data. Poor reproducibility is often an indi- cation of the presence of aggregates. Extensive efforts have been made to eliminate aggregates by the selection of appropriate solvents (9, 62, 63) or by chemically trans- forming the polysaccharides to reduce H-bonding, using derivatives such as carbanilates (64).
3. Sedimentation
Sedimentation methods are of two types, sedimentation equilibrium and sedimentation velocity. The equilibrium technique employs a centrifugal field to create concentra- tion gradients in a polymer solution contained in a special centrifuge cell. For a solute under appropriate conditions (sedimentation equilibrium), sedimentation and diffusion become comparable so that there is no net transport of the
solute. Analysis of the distribution of the solute concen- tration along the centrifugal field at such an equilibrium provides a means to study the MWD and the average MW. For polysaccharides, such an equilibrium distribution is generally achieved in 24–48 hours depending on the nature of the solute and experimental conditions (59).
The basic equation describing the distribution of solute concentration J(r) at sedimentation equilibrium is given for an ideal system as (65):
⫽ (2.10)
where r is the distance of a given point in the cell from the center of the rotor, ω is the rotor speed (rad/s),υis the partial specific volume (ml/g), and ρis the solution den- sity. The solute concentration profile is recorded, usually by a Rayleigh interference optical system, and trans- formed into plots of log J(r) versus r2, from which the
(point) weight average molecular weight can be obtained. The whole-cell Mwcan then be calculated as
Mw⫽ (2.11)
where a and b are the distance from the center of the rotor to the cell meniscus and cell bottom, respectively, and J0 is the initial loading concentration.
Sedimentation equilibrium can cover a very wide range of molecular weights compared to light scattering and osmotic pressure methods. However, since the proce- dure is inherently time consuming and the thermodynamic non-ideality of polysaccharides can complicate interpreta- tion of the measurements, the technique is not frequently applied in polysaccharide research.
As with equilibrium sedimentation, velocity sedimen- tation is based on the principle that the sedimentation rate of a polymer under a centrifugal field is directly propor- tional to its MW and shape. Velocity sedimentation mon- itors the boundary movement during ultracentrifugation by an optical method, from which the sedimentation coef- ficient, and hence MW, can be estimated provided the conformation of the molecule is known. By the use of high angular velocities, initial sedimentation may occur before diffusion effects become important. Compared to equilibrium sedimentation, velocity sedimentation is less time consuming, but can only provide qualitative infor- mation on average MW and MWD.
4. Viscometry
Because of the simple experimental setup and ease of oper- ation, viscometry is extensively used to determine the MW of polysaccharides. The method simply requires the meas- urement of the relative viscosity ηrand polymer concentra- tion of dilute solutions. Experimentally,ηrcan be measured either by a capillary viscometer, a rotational viscometer, or
2RT ᎏᎏω2(1⫺υρ) J(b)⫺ J(a) ᎏᎏJ 0(b2⫺ a2) Mw(r)(1⫺υρ)ω2 ᎏᎏ2RT dlnJ(r) ᎏd(r2) 2.392e-06 6.570e-07 0.0 11.9 sin2(/2) + 10000 c Kc/R (mol g − 1 )
FIGURE 2.3 Zimm plot of tricarbanilate of β-D-(1→3)
a differential viscometer (66). The MW of the polysaccha- rides is then calculated via the Mark-Houwink relationship (Equation 2.18). The Mark-Houwink constants K and αare usually determined experimentally using a series of ideally monodisperse substances with known molecular weights. More discussion of this method will follow (Section V.B). Caution is needed when applying this relative method to polysaccharides with chemical heterogeneity. Any fac- tors that may change chain extension lead to changes in K and αvalues; examples are degree of branching (as with amylopectin and dextrans) and the distribution and/or substitution of certain monosaccharide units (as with algi- nates and galactomannans). The chemical composition and structure of the material under test should resemble those of the calibration substances.
5. Gel Permeation Chromatography
Gel permeation chromatography (GPC) or size exclusion chromatography (SEC) is widely used for the determina- tion of MW and MWD of polysaccharides. In GPC, the polymer chains are separated according to differences in hydrodynamic volume by the column packing material. Separation is achieved by partitioning the polymer chains between the mobile phase flowing through the column and the static liquid phase that is present in the interior of the packing material, which is constructed to allow access of smaller molecules and exclude larger ones. Thus, larger molecules are eluted before smaller ones.
Conversion of the retention (or elution) volume of a polymer solute on a given column to MW can be accom- plished in a number of ways. Narrow MWD standards with known MW, such as pullulan and dextran, may be used to calibrate the column. As with viscometry, the dif- ference in structure between the calibration standards and the tested sample may lead to over- or underestimating the MW. To overcome this, a universal calibration approach may be applied in which the product of intrinsic viscosity [η] and MW, being proportional to hydrodynamic vol- ume, is used (67). For different polysaccharides, a plot of log [η] MW versus elution volume emerges to a common line, the so-called “universal calibration curve.” The cali- bration is usually obtained using narrow MWD standards from which the MW of a test sample can be read, pro- vided the intrinsic viscosity is known.
In the last two decades or so, methods for the deter- mination of MWD have been facilitated by combining GPC with a laser light scattering detector (68, 69). These methods provide absolute measurement of average MW and information on MWD and molecular conformations.
6. Other Methods
There are a number of other less frequently used methods for MW determination of carbohydrates, such as mass spectrometry, end group analysis, and NMR. The readers
are referred to the review by Harding (59) for a detailed discussion of alternative methods on MW determination of carbohydrates. In addition, recent development in AFM has shown that it is a potential means for MW determina- tion of polysaccharides. The power of this approach is that it permits MW measurements of single polysaccharide molecules rather than mixtures of single molecules and aggregates. All the other methods described above deter- mine the apparent MW of samples that often include molecular aggregates. Round et al. (46) found that Mnand Mwobtained from AFM is 2–3 times smaller than that for similar samples measured by conventional techniques.
IV. HYDRATION AND SOLUBILITY OF