Refractive index increment

Concentration fluctuations in solution detected by light scattering turns out to be sufficient to obtain thermodynamic information about polymeric and colloidal systems.

Effectively, the tiny concentration fluctuations between dissolved macromolecules and the solvent depend on their scattering abilities. These abilities differ with the particle’s origin. Titaniumoxide particles, for example, have a refractive index of 2.7 in solid state while organic matter is usually in the range of 1.5-1.9. Polymer coils made out of these different materials will show different scattering behaviors, and titaniumdioxide polymers (if they exist) would show a stronger increase in scattering intensity with increasing concentration than is expected for organic polymers. To consider this effect in our light scattering observations, we need a material constant to describe this behavior named specific refractive index increment, usually called dn/dc.

dn/dc is how much the refractive index of a solution varies for a given increment in concentration, expressed as g/mL.

dn

dcc=0 =lim_c→0

n−n₀ c

(2.29) Usually, these constants are available for several polymers and can be looked up in a number of databases and books^76,77. However, the dn/dc depends strongly on wave-length of the laser, temperature of the solution, the solvent system used and, of course, of the type of polymer; ”just” measuring the dn/dc is not an easy task.

In order to measure the dn/dc, dilute solutions of about 1 mg/mL are required. The change of the refractive index n between solvent and solution is very small if we as-sume a dn/dc of 0.1 mL/g: 0.001 · 0.1 = 10⁻⁴. Normal refractometers of the type checking the purity of an organic liquid are barely precise enough to see these small differences between solvent and solution. At this level of precision, temperature drift becomes a serious concern. To measure the dn/dc precisely, a differential refractometer is needed. A differential refractometer directly observes the refractive index of pure solvent and the solution at the same time, and responds to their difference. Further-more, the refractometer must operate at the same wavelength as the light scattering detector; otherwise the precisely obtained value needs to be wavelength corrected. To inform the reader about which obstacles can appear during the dn/dc determination of chitosan, we will briefly outline the measuring procedure.

Measuring the dn/dc An appropriate amount of chitosan is necessary for preparing precise dilutions of 1 mg/mL. This amount (e.g. for stock solutions about 1 g) should be dried for at least several days to remove any water. It can happen that some water molecules are tightly incorporated in the polymer matrix and thus cannot be evap-orated. Since we are working with natural products, traces of protein, astaxanthin, CaCO3 or NaOH may also appear in the product and are usually not removed. All contaminations reduce the concentration of the chitosan solution to be prepared and can further show significant differences in their optical properties. During dissolution of chitosan, the solvent system (e.g. acetic acid buffer) should be securely capped to avoid evaporation and associated changes of the concentration. It must be taken care on the solvent selection (as mentioned in chapter 1); otherwise, incomplete dissolution is present. If chitosan is solubilized (at least for 24 h), some residual insoluble matter may remain, depending on the purity of the chitosan preparation used. For an opti-mal light scattering experiment, this insoluble matter must be removed by filtration.

There is no need to say that filtrated solutions never show 100% recovery of the target substance, especially if large undissolved particles are present.

After the whole sample preparation, it is not possible to be sure about the real poly-mer concentration at the beginning of the dn/dc experiment. However, the polypoly-mer concentration must be known precisely in order to get realistic dn/dc values.

We have seen that purity of the raw product is of even more importance than an appro-priate selection of a laser beam or a temperature oven, since the latter can be achieved more easily (although it is more expensive). This task becomes even more complex, if

Figure 2.7: Variations of the dn/dc- In different studies about chitosan different dn/dc values were used. The diagram presents values obtained at 436 nm (Wang et al.⁷⁸) and values obtained at 633 nm (Terbojevich et al.⁷⁹, Christensen et al.⁸⁰, Kasaai et al.⁸¹, Chen et al.⁸², Berth et al.⁸³, Schatz et al.⁸⁴) for different chitosan preparations with changing FA.

optical properties of chitosan change with the chemical compositions of the sample.

Variations of the dn/dc Some authors have observed a change of the dn/dc with a change of the F_A, while other reports indicate no dependence of the dn/dc on the F_A (see Fig.2.7). We have to admit that measuring conditions of these reports compared in Fig.2.7 were not identical, and therefore a complete correlation of the data is not expected. However, the difference in the dn/dc between 0.142 and 0.208 is quite large and cannot be explained by a slightly different wavelength (between 436 nm and 546 nm the change should not be higher than 3%⁸⁵) or a 10^◦ higher temperature, although all values may be obtained properly. Several publications also discuss dialyzed and non-dialyzed polyelectrolyte samples showing strong differences in their dn/dc.

At the end we should get at least one reliable dn/dc value in order to be able to calculate the molecular weight of our polymer sample. But which one is to be taken? Since the literature survey could not answer our dn/dc problem sufficiently, let us now have a brief look at familiar polysaccharides.

dn/dc’s of polysaccharides Because there is some uncertainty about which dn/dc value is useful for chitosan analysis, we changed the strategy and took a more thorough look at related polysaccharides. A change in the chemical environment of a polysaccharide is always followed by a change in its dn/dc. A comparison with polysaccharides that have a higher standard of purity control may give an interesting insight into the variability of the dn/dc. So, let us have a look at familiar polysaccharides.

Values for alginate (0.158 - 0.165), amylopectin (0.142 - 0.156), amylose (0.146), car-boxymethylcellulose (0.147 - 0.163), carragenan (0.140), dextran (0.136 - 0.150), ethyl-cellulose (0.154), hyaluronic acid (0.155 - 0.176), starch (0.146 - 0.152) and pullulan (0.137 - 0.147) were found for laser wavelength between 436 - 633 nm in aqueous solu-tion with varying salt contents (all values were taken from⁷⁷). This comparison reveals that completely different polysaccharides show only small changes in their dn/dc. Ex-pecting the same for chitosan, a value comparable to those polysaccharides values was taken for our light scattering experiments (0.163 reported from Rinaudo et al.⁸⁶).

Impact of the dn/dc on molecular weight determination Unfortunately, selection of the dn/dc is not an analytical detail, which becomes important for only some certain cases.

Every light scattering experiment requires this constant, and its impact on the deter-mination of the molecular weight is far from negligible, as shown in Eq. 2.11, Eq. 2.18 and the following equation:

i_s=K_LS·M·(dn/dc)²·c (2.30) The dn/dc enters quadratically to the molecular weight calculation. This calculation also depends on the concentration c of the polymer (obtained by the refractometer) and on a system constant K_LS, which is determined before the measurement with a narrow standard sample (pullulan, dextran or polyethylenoxid). Measuring an unknown sam-ple by light scattering, the molecular weight can be calculated from the light scattering intensity i_s, if the previously mentioned values are known.

Using a dn/dc of 0.142⁸⁰for the dn/dc, the M_W calculation of a high molecular weight chitosan sample, we receive a molecular weight of 1098 kg/mol. Changing the value to 0.208⁸³for the same chromatography data, the M_W decreases to 750 kg/mol. The use of published dn/dc values on identical data leads, therefore, to a drastic change in the molecular weight of up to 32%! Thus, comparison of molecular weight data obtained by light scattering must include information about the dn/dc; otherwise, a comparison will never show conformity when two different dn/dc’s were used.