Air Pollution Zones and Harmful Pollution Levels of Alkaline Dust for Plants

For characterisation of landscapes in north-eastern Estoniaaffected by alkaline oil shale fly ash and cement dust the zonation-method based on average annual (C _y) and short-termconcentrations of pollutants in the air was used, as well as on deposition loads of dust and Ca²⁺. In the overground layer of atmosphere the zones with different air pollution loads were distinguished. A comparative analysis of pollution zones characteristics and biomonitoring data revealed that for sensitive lichen the dangerous level of alkaline dust in the air, introducingthe degradation of Sphagnum sp. at the level of C _y of dust 10–20 g m^-3 and at 0.5–1 hr maximums 100–150 g m^-3. For Scots pine (Pinus sylvestris L.) and Norway spruce (Picea abies (L.) Karst.) this limited concentration (decline of growth parameters) of cement dust is correspondingly following: 30–50 g m^-3 and 150–500 g m^-3, in case of fly ash the limit level of C _y amounting 100 g m^-3. Daily deposition load of Ca²⁺ should not exceed approximately 4.5–15 mg m^-2 for lichen; for conifers the harmful pollution load is higher – >22 mg m^-2.     

An Automated Wet Deposition System to Compare the Effects of Reduced and Oxidised N on Ombrotrophic Bog Species: Practical Considerations

Critical N loads for ombrotrophic bogs, which often contain rare and N-sensitive plants (especially those in lower plant groups: lichens, mosses and liverworts), are based on very few experimental data from measured, low background N deposition areas. Additionally the relative effects of reduced versus oxidised N are largely unknown. This paper describes an automated field exposure system (30 km S. of Edinburgh, Scotland) for treating ombrotrophic bog vegetation with fine droplets of oxidised N (NaNO₃) and reduced N (NH₄Cl). Whim Moss exists in an area of low ambient N deposition (ca. 8 kg N ha^–1 y^–1), the sources and quantification of which are described. The wet N treatment system is run continuously, and is controlled/activated by wind speed and rainfall to provide a unique simulation of real world treatment patterns (no rain=no treatment). Simulated precipitation is supplied at ionic concentrations below4mMin rainwater collected on site. Treatments provide a replicated dose response to 16, 32 and 64 kg N ha^–1 y^–1 adjusted for ambient deposition (8 kg N ha^–1 y^–1). The 16 and 64 kg N ha^–1 y^–1 are duplicated with a P+K supplement. Baseline soil chemistry and foliar nutrient status was established for all 44 plots for Calluna vulgaris, Sphagnum capillifolium, Hypnum jutlandicum and Cladonia portentosa.     

A Conceptual Model of Spatially Heterogeneous Nitrogen Leaching from a Welsh Moorland Catchment

Soil- and stream-water data from the Plynlimon research area, mid-Wales, have been used to develop a conceptual model of spatial variations in nitrogen (N) leaching within moorland catchments. Extensive peats, in both hilltop and valley locations, are considered near-complete sinks for inorganic N, but leach the most dissolved organic nitrogen (DON). Peaty mineral soils on hillslopes also retain inorganic N within upper organic horizons, but a proportion percolates into mineral horizons as nitrate (NO ₃ ^– ), either through incomplete immobilisation in the organic layer, or in water bypassing the organic soil matrix via macropores. This NO ₃ ^– reaches the stream where mineral soilwaters discharge (via matrix throughflow or pipeflow) directly to the drainage network, or via small N-enriched flush wetlands. NO ₃ ^– in hillslope waters discharging into larger valley wetlands will be removed before reaching the stream. A concept of catchment nitrate leaching zones is proposed, whereby most stream NO ₃ ^– derives from localised areas of mineral soil hillslope draining directly to the stream; the extent of these zones within a catchment may thus determine its overall susceptibility to elevated surface water NO ₃ ^– concentrations.     

Quantifying dry NH3 deposition to an ombrotrophic bog from an automated NH3 field release system

Providing an accurate estimate of the dry component of N deposition to low N background, semi-natural habitats, such as bogs and upland moors dominated by Calluna vulgaris is difficult, but essential to relate nitrogen deposition to effects in these communities. To quantify the effects of NH₃ inputs to moorland vegetation growing on a bog at a field scale, a field release NH₃ fumigation system was established at Whim Moss (Scottish Borders) in 2002. Gaseous NH₃ from a line source was released along of a 60 m transect, when meteorological conditions (wind speed >2.5 m s^–1 and wind direction in the sector 180–215°) were met, thereby providing a profile of decreasing NH₃ concentration with distance from the source. In a complementary study, using a NH₃ flux chamber system, the relationships between NH₃ concentrations and cuticular resistances were quantified for a range of NH₃ concentrations and micrometeorological conditions for moorland vegetation. Cuticular resistances increased with NH₃ concentration from 11 s m^–1 at 3.0 g m^–3 to 30 s m^–1 at 30 g m^–3. The NH₃ concentration data and the concentration-dependent canopy resistance are used to calculate NH₃ deposition taking into account leaf surface wetness. The implications of using an NH₃ concentration-dependent cuticular resistance and the importance for refining critical loads are discussed.     

On Sand and Duststorms and Associated Significant Dustfall Observed in Chongju-Chongwon,Korea during 1997–2000

Monitoring of the occurrence of sandstorms and dustfallphenomena from 1997 to 2000 was carried out. We refer tosandstorms, duststorms and blowing sand as the phenomenaoccurring in the source region, while significant dustfall is thephenomenon that occur in the sink area. It was noted that while the sandstorms in deserts and loess in NW-N China and Mongolia occurred any time during the year while severe sandstorms occurred frequently from March to May after the springthaw. The wind erosion in the source region usually occurred withwind speeds greater than 8 ms^-1. However, severe sandstorm phenomenon occurred with wind greater than 15 ms^-1 for at least 3 hr or more. In the source regions, sandstorms occurred over60–120 days per year. In Mongolia, the observation of thenumber of sandstorm days decreased due to the increase in rainy days.When a dust cloud from a desert reached the sink region,significant dustfall in the Korean Peninsula occurred due tothe lack of strong winds. We defined the episode ofsignificant dustfall (SD) with the following values: TSP250, PM₁₀ 190 g m^-3 and visibility 6.5 km or less. In Korea, 8–12 episodes of SD occurred per yearwith 12 to 22 SD days. The maximum concentrations of TSP recorded were 989–1396 g m^-3 with PM₁₀ values of 861–996 g m^-3 and with the lowestvisibility of 1.4–1.6 km.     

Assessing Aerobic Biodegradability of Plastics in Aqueous Environment by GC-Analyzing Composition of Equilibrium Gaseous Phase

Testing biodegradability of plastics under varied conditions of the environment as well as under laboratory conditions in accordance with valid international standards is very laborious, lengthy and often also economically demanding. For this reason, applicability was verified of gas chromatography to analyze gaseous phase when investigating the biodegradation course of plastics in an aqueous environment as an alternative to customary employed methods. A mathematical model of acid–basic CO₂ equilibrium in a gas–liquid system was worked out, enabling to determine quantity of produced CO₂ through chromatographic analysis of gaseous phase, in dependence on ratio of liquid and gas phase volumes (V _l/V _g) and on actual pH of liquid phase. Experimental conditions for organizing the tests were optimized. A ratio that proved suitable was V _l/V _g ≅ 0.1 at pH ≈ 7.1 of liquid phase. Under these test conditions, biodegradability of model samples, PHB, Gellan gum and Xanthan gum, was explored; course of biodegradation was studied through produced CO₂ (values ) determined by analyzing gaseous phase through gas chromatography on the one hand, and through customary “titration” procedure on the other. With water-soluble polymers, the decrement in dissolved organic carbon (values D _DOC) was also studied. Difference between values does not exceed 5%. The procedures in question are alternative “substituting” procedures for observing course of aerobic biodegradation of substances in an aqueous environment.     

Study on the conversion of waste plastics/petroleum resid mixtures to transportation fuels

Catalytic coprocessing of model and waste plastics with light Arabian crude oil residue was investigated using NiMo/Al₂O₃, ZSM-5, FCC, and hydrocracking catalysts. Reaction systems that were studied included low density polyethylene (LDPE), high density polyethylene (HDPE), polystyrene (PS), and polypropylene (PP). A series of single (plastic/catalyst) and binary (plastic/resid/catalyst) reactions were carried out in a 25-cm³ micro autoclave reactor under different conditions of weight and type of catalyst, duration, pressure, and temperature. The optimum conditions selected for our work were: 1% catalyst by weight of total feedstock weight, 60min reaction time, 8.3Mpa of H₂, and 430°C. The product distribution for the binary system using plastic and petroleum residue provided some encouraging results. High yields of liquid fuels in the boiling range of 100°–480°C and gases were obtained along with a small amount of heavy oils and insoluble material such as gums and coke. In general, this study helps to demonstrate the technical feasibility of upgrading both waste plastics and petroleum resid, as well as an alternative approach to feedstock recycling.     

Modelling of Air Quality with CAMx: A Case Study in Switzerland

The three-dimensional Eulerian model CAMx (Comprehensive Air QualityModel with Extensions) was applied for the first time to simulate bothgaseous and particulate photochemical air pollution in Switzerland during July 28–30, 1993. The meteorological input data were prepared using the Systems Applications International Mesoscale Model (SAIMM). The CAMx model results were compared with the measurements carried out at ground level andfrom airborne measuring platforms within the frame of the Swiss POLLUMET research programme. In general, the CAMx performance for gaseous species wasfound to be better than that of the previously used Urban Airshed Model (UAM)and the Variable Grid Urban Airshed Model (UAM-V). The most significant improvement for the gaseous species is in the prediction of HNO₃ concentrations, due to the inclusion of aerosol chemistry. Aerosol species such as NO₃ ^-, NH₄ ⁺, SO₄ ^2-, and secondary organic aerosols were calculated in one particle size range (0.04–2.5 m) and compared with a few measurements available. Although July 29 was reasonably well simulated, overestimated wind speeds by SAIMM for July 30 caused a too fast transport of pollutants. Similarly to measurements, significant spatial correlation of the secondarily formed aerosols with ozone and formaldehyde is found in the afternoon.     

Novel Biobased Polyurethanes Synthesized from Soybean Phosphate Ester Polyols: Thermomechanical Properties Evaluations

Biobased polyurethanes from soybean oil–derived polyols and polymeric diphenylmethane diisocyanate (pMDI) are prepared and their thermomechanical properties are studied and evaluated. The cross-linked biobased polyurethanes being prepared from soy phosphate ester polyols with hydroxyl contents ranging from 122 to 145 mg KOH/g and pMDI within 5 min of reaction time at 150°C in absence of any catalyst show cross-linking densities ranging from 1.8 × 10³ to 3.0 × 10³ M/m³, whereas glass transition temperatures vary from approximately 69 to 82°C. The loss factor (tan ) curves show single peaks for all these biobased polyurethanes, thus indicating a single-phase system. The storage moduli (G) at 30°C range from 4 × 10⁸ to 1.3 × 10⁹ Pa. Upon postcure at 150°C, the thermomechanical properties can be optimized. Cross-link densities are improved significantly for hydroxyl content of 139 and 145 mg KOH/g at curing time of 24 h. Similarly, glass transition temperature (T_g) and storage moduli around and after T_g are increased. Meanwhile, tan intensities decrease as result of restricted chain mobility. Longer exposure time (24 h) induces thermal degradation, as evidenced by thermogravimetric analysis (TGA). The dynamic mechanical (DMA) analysis shows that postcure at 100°C for times exceeding 24 h also leads to improved properties. However, cross-linking densities are lower compared to postcure carried out at 150°C.     

The Application of Stable Isotopes for Assessing the Hydrological, Sulfur, and Iron Balances of Acidic Mining Lake ML 111 (Lusatia, Germany) as a Basis for Biotechnological Remediation

Stable isotope (¹⁸O–H₂O, ²H–H₂O ³⁴S–SO₄ ^2-) andhydrochemical data (SO₄ ^2-, Fe-concentrations) have beenused to estimate the annual groundwater inflow and outflow of mining lake ML 111 and to calculate the total amount of dissolvedsulfate and iron that is carried into the lake by groundwater. The hydrological balance suggests an annual groundwater inflow of 23 700 m³ and an annual groundwater outflow of 15 700 m³. The calculation of the sulfur and iron balances yielded an annual sulfate input of 37 800 kg and an annual iron input of 7000 kg with the groundwater inflow. Furthermore it was shown that significant fluxes of these elements go into the lake sediments which results in continuous release of acidity in the lake water.     

Biodegradation of Low Molecular Weight Organic Acids in a Limed Forest Soil

The effect of liming (3.45 and 8.75 t ha^-1 dolomite; 16 yr after application) on the biodegradation of three low molecular weight organic acids (citrate, oxalate and propionate) in forest soils was investigated. The concentration of organic acids in the soil solution followed the series propionate > citrate > oxalate with liming having no significant impact on soil solution concentrations (mean organic acid concentration = 8.7 ± 2.3 M). Organic acid mineralization by the soil microbial community was rapid in surface organic horizons (mean half-life for citrate = 2–6 h), with biodegradation rate gradually declining with soil depth. Concentration-dependent biodegradation studies (0 to 350 M) showed that the mineralization kinetics generally conformed well to a single Michaelis–Menten equation with V_max values following the series oxalate > citrate > propionate (mean = 9.8 ± 1.0 nmol g^-1 h^-1) and K_M values following the series oxalate = citrate > propionate (mean 168 ± 25 M). The V_max values declined with soil depth, which was consistent with a general reduction in microbial activity down the soil profile. Liming induced a significant increase in V_max for citrate with no change for propionate and reduction in V_max for oxalate. The latter was probably due to adsorption and precipitation of Ca-oxalate making it unavailable for microbial uptake. The higher adsorption/precipitation capacity for oxalate in the limed soils was confirmed by adsorption isotherms. Generally, liming increased soil microbial activity by approximately 10 to 35% with calculations based on soil solution concentrations indicating that organic acid mineralization constituted approximately 3 to 15% of the total soil respiration.     

On East Asian Sand and Duststorms and Associated Significant Dustfall Observed from January to May 2001

Monitoring of dust pollution at the western shore of Tae-ahn Peninsula (TAP) and in the Chongju area of central Korea was carried out from January to May 2001. It was found that in Koreathere were 9 cases of sand and duststorms (DS) and 16 associatedsignificant dustfall (SD) days. Observed maximum concentrations of DS and SD coming from NW China and Mongolia were in the rangeof 300–920 for TSP, 200–690 for PM₁₀ and 100–170 g m^-3 for PM_2.5.Satellite measurements clearly showed the formation and subsequent movement of DS to the Korean Peninsula and onward to the Korea East Sea, Japan and the Gulf of Alaska. According to satellite image analysis of dust clouds there were abundant coarse particles, measuring in size of 11.0 m. Medium-sizedparticles measuring in the range of 3.5–7.0 were also prevalent,while fine particles of less than 2.0 m were less distinctive in reflectivity. Measured values of PM_2.5 were alsorelatively low with SD events.The measured average pH values of dusty precipitation associatedwith DS were 7.24. Alkaline precipitation can play a `temporary'role in the neutralization of acidified soil until the subsequentevent of acidic rain. The new selection criteria of SD days from PM_2.5 at 85 g m^-3, PM₁₀ 190 g m^-3 and TSP 250 g m^-3 are recommended on dust pollution occurring from the invasion of a DS elsewhere.     

Solid State Reactions of Potato Starch with Urea and Biuret

Reaction of granular potato starch with urea and biuret resulted in the formation of products, which were soluble neither in cold nor boiling water. The net reaction was a monosubstitution of the hydrogen atom in one hydroxyl group in each D-glucose unit of starch with the either CO–NH₂ or CO–NH–CO–NH₂ moiety, respectively. Properties of the products, particularly these with urea, depended on the mode of reaction. Reactions were carried out in the microwave oven as well as with convection heating. The products retained the granular form of starch but a vast majority of granules were damaged. -Amylolysis of those materials revealed that their susceptibility to the enzyme increasing in the order: starch-amylolysis with simultaneous insolubility in water make these products suitable as ruminant fodder and, eventually, biodegradable material.     

Lowest Effect Levels of Lead and Mercury on Decomposition of Mor Layer Samples in a Long-Term Experiment

Indications of possible negative effects of lead (Pb) and mercury(Hg) on microbial respiration in Southern Swedish forest humus layers led to experiments on dose-response relationships by additions of metal salts in the laboratory. Respiration rates andweight loss due to decomposition of organic material were measured. For relevance to field situations metal doses were low,the time span was long, 550 days including freeze storage, and microbial activity was kept up by plant litter additions. We looked for effects of Pb and Hg at levels moderately elevated above the Southern Swedish reference, as well as combined effectsof Pb + Hg. A reduction in respiration and decomposition of10% was found at about 225–245 g g^-1 of total Pb, i.e. ata Pb level elevated 3.5 times. Although small effects of Hg werefound even at the lowest dose level, 10% inhibition of microbialactivity appeared temporarily at about 2–3 g g^-1 of total Hg, i. e. at 6–8 times the reference level. There were nolong-term additive effects of Pb and Hg on decomposition. Type of anion had a strong influence on the test, chlorides of Pbbeing more toxic than nitrates. Long-term monitoring and maintenance of microbial activity during the experiment were prerequisites for the occurrence of effects at low metal levels.     

Modelling and Optimization of Uranium (VI) Ions Adsorption Onto Nano-ZnO/Chitosan Bio-composite Beads with Response Surface Methodology (RSM)

Nano-ZnO-chitosan bio-composite beads were prepared for the sorption of \({\text{UO}}_{2}^{{2+}}\) from aqueous media. The resulting nano-ZnO/CTS bio-composite beads were characterized by TEM, XRD etc. The sorption of \({\text{UO}}_{2}^{{2+}}\) by bio-composite beads was optimized using RSM. The correlation between four variables was modelled and studied. According to RSM data, correlation coefficients (R²?=?0.99) and probability F-values (F?=?2.24?×?10^??10) show that the model fits the experimental data well. Adsorption capacity for nano-ZnO/CTS bio-composite beads was obtained at 148.7 mg/g under optimum conditions. The results indicate that nano-ZnO/CTS bio-composite beads are appropriate for the adsorption of \({\text{UO}}_{2}^{{2+}}\) ions from aqueous media. Also, the suitability of adsorption values to adsorption isotherms was researched and thermodynamic data were calculated.     

Application of the rescue number to the evaluation of remediation technologies for contaminated ground

An improved rescue number, RN_SOIL, which is an indicator for evaluating remediation technologies for contaminated ground that is based on both the risk and the remediation cost, is proposed as a tool of risk communication. The risk posed by contaminated ground is indicated by the figure of treatment priority at time t, FTP(t), which represents the human health risk as the number of people affected by the contaminated ground at time t during the remediation process. The calculation of the value of FTP(t) is based on exposure to contaminants that have migrated through environmental media from the contaminated ground, and is estimated by using a CalTOX model and the Monte Carlo method. The integration of FTP(t) with time, which represents the cumulative number of people affected by the contaminated ground, is used to estimate the performance of individual remediation technologies in risk reduction. The figure of unprocessibility for waste (FUW), which represents difficulties in remediation, is expressed as the remediation cost. FUW is estimated by using actual costs per unit volume of remediated soil. As an overall performance value, the rescue number for each remediation technology for contaminated ground (RN_SOIL) is calculated by multiplication of the integral FTP(t) by FUW. Smaller values of RN_SOIL are judged to indicate a better technology. The rescue index (RI), calculated as the ratio of the reduction of the integral FTP(t) to FUW, indicates the cost-effectiveness of the remediation technologies. Successful estimation of the indices (FTP(t), integral FTP(t), FUW, RN_SOIL and RI) demonstrate the usefulness of these indices in risk communication.Part of this paper was presented at 13th meeting of Japan Society of Waste Management Experts (2002)     

Properties and biodegradability of chain-extended copoly(succinic anhydride/ethylene oxide)

Chain-extension reactions were carried out using titanium-iso-propoxide (TIP) as a catalyst for a series of polyesters or copolyesterethers with low molecular weights (M _n =1500–10,000) synthesized by the ring-opening copolymerization of succinic anhydride (SA) with ethylene oxide (EO). The copolymers having aM _n from 25,000 to 50,000 of different properties were obtained. Both the melting point (T _m ) and the fusion heat (H), which indicate the crystallinity of the copolymers, rose with an increase in SA content in the copolymers. Semitransparent films were prepared by compression molding of the copolymers. The biodegradation of the copolymer films was evaluated by enzymatic hydrolysis by lipases and by an aerobic gas evolution test in standard activated sludge. The hydrolyzability of these copolymers by three kinds of lipases was affected by their copolymer composition SA/EO, form, andM _n . The copolyesterether (SA/EO=43/57,M _n =48,900) was more easily biodegraded by standard activated sludge compared to the polyester (SA/EO=47/53,M _n =36,300).Presented at the Pacifichem-95, December 17–22, 1995, Honolulu, Hawaii.     

Crystallization behavior of predominantly syndiotactic poly(β-hydroxybutyrate)

Predominantly syndiotactic poly(-hydroxybutyrate), syn-PHB, of variable syndioregularity (syndyad fractions 0.59, 0.62, 0.64, and 0.71) and molecular weight was prepared by the dibutyltin dimethoxide catalyzed ring opening of racemic-butyrolactone (BL). The crystallization behavior of the syn-PHB polymers was investigated by DSC and X-ray diffraction analyses. DSC of films after melting and annealing showed at least one, and often two distinct melting transitions occuring over a broad (often 40°C) temperature range. These results indicate that syn-PHB chain segments of variable syndioregularity form crystalline regions with very different thermodynamic stabilities. Maximum degrees of crystallinity for melt annealed 0.64- and 0.71-syn-PHB was observed at an annealing temperature (T _c ) of 30°C. AtT _c values at 45°C and higher, crystallization of relatively lower syndioregular chain segments was apparently excluded to variable degrees dependent onT _c and sample syndiotactic dyad content. After crystallization of syn-PHB samples at elevated temperatures, ambient temperature annealing resulted in an observed lower temperature melting transition at 50°C. This result showed little to no dependence on syn-PHB syndio-regularity andT _c . Both solution precipitated 0.62-syn-PHB and 0.71-syn-PHB have WAXS patterns with poorly resolved crystalline reflections superimposed on amorphous haloes indicating low levels of crystallinity (17% and 25%, respectively) and poorly formed crystals. Isothermal crystallization monitored by DSC showed that the syn- and natural origin PHB showed fastest crystallization rates at temperatures between 50°C and 70°C and 60°C and 90°C, respectively. From the dependence of the higher melting transition onT _c it was determined that the equilibrium melting temperatures for 0.62-syn-PHB (M _n =83,700 g/mol) and a 0.64-syn-PHB (M _n =11,900 g/mol) were 157 and 154°C, respectively. An Avrami analysis of syn-PHB yielded results similar to that found for natural origin PHB indicating that crystal growth occurs by a two-dimensional mechanism.Guest Editor: Dr. Graham Swift, Rohm & Haas.     

Fast and Living Ring-Opening Polymerization of l-Lactide Initiated with In-situ–Generated Calcium Alkoxides

The ring-opening polymerization of l-lactide with calcium alkoxides generated in-situ from bis(tetrahydrofuran)calcium bis[bis(trimethylsilyl)amide] and 2-propanol are presented. The polymerization in THF at room temperature proceeds rapidly and in a living manner, giving poly(l-lactide)s of controlled molecular weight, low polydispersity, and tailored end-functionalities. Kinetic studies show the absence of an induction period and a pseudo-first order rate constant of 6.41 L mol^–1 min^–1, which is significantly higher than for related Y₅(-O)(O ⁱ Pr)_13– or aluminum alkoxide-initiated polymerizations. The initiation involves a two-step process: (1) alcoholysis of bis(tetrahydrofuran)calcium bis[bis(trimethylsilyl)amide] to give the corresponding calcium alkoxide and (2) ring-opening of l-lactide via acyl-oxygen cleavage and insertion into the calcium-alkoxide bond. In the presence of excess alcohol, fast and reversible exchange between free alcohol molecules and coordinated alkoxide ligands takes place. This allows tuning of the poly(l-lactide) molecular weight over a wide range.     

Kinetics of Aerobic Polymer Degradation in Soil by Means of the ASTM D 5988-96 Standard Method

The standard test method ASTM D 5988-96 for determining the degree and rate of aerobic biodegradation of plastic materials in contact with soil was applied to poly(3-hydroxybutyrate) and poly(-caprolactone). The method proved to be reliable and supplied reproducible measurements of CO₂ production, provided potassium (instead of barium) hydroxide was used as a trapping solution. The trends of CO₂ evolution, as a function of time, observed for the degradation of polymer powders in soil are similar to those predicted by simple first order kinetics in solution. The experimental data are described by a Michaelis–Menten type model, which accounts for the heterogeneity of the polymer-soil system. The kinetic equation deduced predicts the degradation rate to the proportional to the exposed polymer surface area.